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In this chapter students will understand the concepts and logics behind calculating the factors and multiples of different numbers. Exercise 3. Column 1 Column 2. The numbers 13 and 31 are prime numbers.

Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to We know that numbers which have only two factors 1 and the number itself are prime numbers and the other numbers which have more than two factors are called composite numbers.

Write seven consecutive composite numbers less than so that there is no prime number between. There are seven composite numbers between 89 and 97 such that there is no prime number between. These seven composite numbers are:. Using divisibility tests, determine which of the following numbers are divisible by 2, by 3, by 4, by 5, by 6, by 8, by 9, by 10, by 11 Say, Yes or No.

Using divisibility tests, determine which of following numbers are divisible by 4; by 8. Here, last three digits form which is not divisible by 8 so the numbre is not divisible by 8. Here, last two digits form 52 which is divisible by 4. So the number is also divisible by 4. Here, last three digits form which is divisible 8 so the number is also divisible by 8. Here, last three digits form which is not divisible by 8 so the number is not divisible by 8.

Here, last two digits form 59 which is not divisible by 4 so byjus class 6 maths chapter 3 read number is not divisible by 4. Here, last two digits form 84 which is divisible by 4 so the number is also divisible by 4.

Here, last three digits form which us divisible by 8 so the number is also divisible by 8. Here, last three digits form which is not divisible by 8 so the number is also not divisible by 8. Here, last two digits form 50 which is not divisible by 4 so the number is also not divisible by 4. Using divisibility tests, determine which of the following numbers are divisible by Since the given number is not divisible by both 2 and 3 therefore, it is not divisible by 6.

We know that a number is divisible by 11 if the difference between the sum of the digits at odd places from the right and the sum of the digits at even places from the right of the number is either 0 or divisible by Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3. Write a digit in the blank space of each of the following numbers so that the numbers formed is divisible by A number is divisible by both 5 and By which other will that byjus class 6 maths chapter 3 read be always divisible?

If number is divisible by another number, then it is also divisible by each of the factors of that number. Hence the number which is divisible by 12 will also be divisible by 1, 2, 3, 4, 6 and And we know that if number is divisible by another number, then it is also divisible by each of the factors of that number.

Which factors are not included in the prime factorisation of a composite number? Write the greatest 4-digit number and express it in terms of its prime factors. Write the smallest 5-digit number and express it in the form of its prime factors.

Find all the prime factors of and arrange them in ascending order. Now state the relations, if any, between the two consecutive prime factors. The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

The sum of two consecutive odd numbers is divisible by 4. Similarly, a number is divisible by both 4 and 6. If not, give an example to justify your answer. I am the smallest number, having four different prime factors. Can you find me? Renu purchases two bags of fertiliser of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertiliser exact number of times.

Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can cover the distance in complete steps? The length, breadth and height of a room are cm, cm and cm respectively.

Find the longest tape which can measure the three dimensions of the room exactly. Determine the smallest 3-digit number which is exactly divisible by 6, 8 and The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and seconds respectively.

If they change simultaneously at 7 a. Three tankers contain litres, litres and litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of the three containers exact number of byjus class 6 maths chapter 3 read. Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.

Since, is the smallest number which is exactly divisible by 18, 24 and 32 but it is byjus class 6 maths chapter 3 read a 4-digit number. Observe a common property in the obtained LCMs. Is LCM the product byjus class 6 maths chapter 3 read two numbers in each case? Here, in all of the questions given above the LCM of numbers comes to be equal to their product. Actually, when two numbers are co-prime their LCM is equal to their product.

Find the LCM of the following numbers in which one number is the factor of the. Here is all the questions given above, we observe that the LCM of the byjus class 6 maths chapter 3 read numbers, with one number being a factor byjus class 6 maths chapter 3 read the other, is the greater number.

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i'm considering short byjsu upon a vessel constructing academy down in devon. Interjection in your support. Reduce as well as insert a rug play (the building of your dock) to a physique with rug screws. I did. With a doubt inside of a automaker's future For effectivity purposes, we lift in the freshwater hose by approach of a porthole (that's the window for non-boating people) as well as goal it down a lavatory.

Provide feedback to us for betterment of website. We are working to make study easier in all the subjects. In 6 Maths Chapter 9 Data Handling, we will study about the ways to record raw data and how to use this data to interpret the result and predict further results.

Organization of data using tally marks and frequency distribution then interpret it into pictograph and bar graph. Pictograph: A pictograph represents data through pictures of objects. It helps answer the questions on the data at a glance. Bar Graph: Bars of uniform width are drawn horizontally or vertically with equal spacing between them and then the length of each bar represents a particular number.

Such method of representing data is called a bar diagram or a bar graph. To represent this we use the process of choosing a scale for the graph. We should learn how to read a given bar graph.

Note: To get a particular information from the given data quickly, the data can be arranged in a tabular form using tally marks. No login and password is required on this website. Answer: A number with 3 or more digits is divisible by 4 if the number formed by its last two digits is divisible by 4.

A number with 3 or more digits is divisible by 8 if the number formed by its last three digits is divisible by 8. The number is not divisible by 8. Hence, the number is divisible by 4 and 8. Hence, the number is not divisible by 4. Hence the number is divisible by 4 and 8. The number is divisible by 4. Q3 Using divisibility tests, determine which of the following numbers are divisible by 6: a b c d e f g h i j Answer: a Since the last digit Of the number is 4, it is divisible by 2.

On adding all the digits of the number, the sum obtained is Since 27 is divisible by 3, the given number is also divisible by 3. As the number is divisible by both 2 and 3, it is divisible by 6. Since the last digit of the number is 8, it is divisible by 2. Since 16 is not divisible by 3, the given number is also not divisible by 3.

As the number is not divisible by both 2 and 3, it is not divisible by 6. The last digit of the number is 5, which is not divisible by 2. Therefore, the given number is also not divisible by 2. Since 15 is divisible by 3, the given number is also divisible by 3.

The last digit of the number is 3, which is not divisible by 2. On adding all the digits Of the number, the sum obtained is Since the last digit of the number is 2, it is divisible by 2. Since 20 is not divisible by 3, the given number is also not divisible by 3. Since the last digit of the number is O, it is divisible by 2.

Since the last digit of the number is 4, it is divisible by 2. Since 30 is divisible by 3, the given number is also divisible by 3. Since the last digit of the number is 3, it is not divisible by 2. Since 19 is not divisible by 3, the given number is also not divisible by 3. Since 21 is divisible by 3, the given number is also divisible by 3. Since 23 is not divisible by 3, the given number is also not divisible by 3.

Q4 Using divisibility tests, determine which of the following numbers are divisible by a b c d e f Therefore, is divisible by Therefore, is not divisible by To make the number divisible by 3, the sum of its digits should be divisible by 3. The smallest multiple of 3 which comes after 19 is As 24 is already divisible by 3, the smallest number that can be placed here is 0.

If we put 9, then the sum of the digits will be 33 and as 33 is divisible by 3, the number will also be divisible by 3.

The number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is divisible by Q Find the common factors of: a 8, 20 b 9, Answer: The common factors of the following are: a 8, Hence, the common factors are. Q1 Find the common factors of : a 20 and 28 b 15 and 25 c 35 and 50 d 56 and Answer: a 20 and Q2 Find the common factors of : a 4, 8 and 12 b 5, 15 and Answer: a 4,8, Q3 Find the first three common multiples of : a 6 and 8 b 12 and Answer: a 6 and 8.

Q4 Write all the numbers less than which are common multiples of 3 and 4. Q5 Which of the following numbers are co-prime? Answer: a 18 and As these numbers have a common factor other than 1, the given two numbers are non co-prime. Q6 A number is divisible by both 5 and By which other numbers will that number be always divisible?

As the common factor of these numbers is 1, the given two numbers are coprime and the number will also be divisible by their product, i. Q7 A number is divisible by By what other numbers will that number be divisible? Answer: Since the number is divisible by 12, it will also be divisible by its factors i.

Clearly, 1, 2, 3, 4, and 6 are numbers other than 12 by which this number is also divisible. Q Write the prime factorizations of 16, 28, Answer: prime factorizations of. Q1 Which of the following statements are true? Answer: a False as 6 is divisible by 3, but not by 9. Q2 Here are two different factor trees for Write the missing numbers. Q3 Which factors are not included in the prime factorization of a composite number?

Answer: 1 is the factors which are not especially included in the prime factorization of a composite number. When the number is divisible by 2 co-prime numbers then they are divisible by their product.

When two given numbers are divisible by a number, the sum is also divisible by number. When 2 given numbers are divisible by number then its difference is divisible by that number. Q4 Write the greatest 4-digit number and express it in terms of its prime factors. Q5 Write the smallest 5-digit number and express it in the form of its prime factors. Q6 Find all the prime factors of and arrange them in ascending order.

Now state the relation, if any; between two consecutive prime factors. Answer: Prime factors of are -7,13, Q7 The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples. Q8 The sum of two consecutive odd numbers is divisible by 4.

Q9 In which of the following expressions, prime factorization has been done? Answer: in factorization, we don't write composite numbers. All the factors should be prime numbers in this method. As we know that 4 is a composite number. Hence This is not a prime factorization. There is no composite number. Hence This is prime factorization. There is not a composite number in this process of factorization. In this factorization, 2 and 3 are prime numbers, but 9 is a composite number.

Q10 Determine if is divisible by Test the divisibility of the number by 5 and 9]. As the sum of the digits of is divisible by 9, therefore. Since the number is divisible by 5 and 9 both, it is divisible by Q12 I am the smallest number, having four different prime factors. Can you find me? Answer: Since it is the smallest number of such type, it will be the product of 4 smallest prime numbers.

Q Find the HCF of the following: i 24 and 36 ii 15, 25 and 30 iii 8 and 12 iv 12, 16 and Answer: i 24 and Q1 Find the HCF of the following numbers : a 18, 48 b 30, 42 c 18, 60 d 27, 63 e 36, 84 f 34, g 70, , h 91, , 49 i 18, 54, 81 j 12, 45, Answer: a 18, Q2 What is the HCF of two consecutive a numbers?

Answer: a 1 e. Is the answer correct? If not, what is the correct HCF? Answer: No, the answer is not correct. Q1 Renu purchases two bags of fertilizer of weights 75 kg and 69 kg.

Find the maximum value of weight which can measure the weight of the fertilizer exact number of times. Hence the maximum value of weight which can measure the weight of the fertilizer exact number of times is 3. Q2 Three boys step off together from the same spot.

Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can cover the distance in complete steps? Q3 The length, breadth and height of a room are cm, cm and cm respectively. Find the longest tape which can measure the three dimensions of the room exactly. Q4 Determine the smallest 3-digit number which is exactly divisible by 6, 8 and Hence, the smallest 3-digit number which is exactly divisible by 6, 8, and 12 is Q5 Determine the greatest 3-digit number exactly divisible by 8, 10 and Answer: CM of 8, 10 and Hence, the greatest 3-digit number exactly divisible by 8, 10, and 12 is Q6 The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and seconds respectively.

If they change simultaneously at 7 a. They will change together after every seconds i. Q7 Three tankers contain litres, litres and litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of the three containers exact number of times. Hence the maximum capacity of a container that can measure the diesel of the three containers the exact number of times is Q8 Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.

Answer: LCM of 6, 15, Q9 Find the smallest 4-digit number which is divisible by 18, 24 and Answer: LCM of 18, 24 and Therefore, the smallest 4-digit number which is divisible by 18, 24, and 32 is Is LCM the product of two numbers in each case? Yes, it can be observed that in each case, the LCM of the given numbers is the product of these numbers.

When two numbers are co-prime, their LCM is the product of those numbers. Also, in each case, LCM is a multiple of 3. Q11 Find the LCM of the following numbers in which one number is the factor of the other. Yes, it can be observed that in each case, the LCM of the given numbers is the larger number. When one number is a factor of the other number, their LCM will be the larger number. Chapters No. Chapters Name. Chapter - 1. Chapter - 2.

Chapter - 3. Chapter - 4. Chapter - 5. Chapter - 6. Chapter - 7. Chapter - 9. Chapter

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