Playing with Numbers Class 6 Maths Questions | Worksheet takshilalearning.com/playing-with-numbers-class-6-maths-questions-worksheet/ December 8, 2021
Playing with Numbers Class 6
Playing with Numbers NCERT Class 6 Maths Questions and Answers This worksheet is for class 6 maths, comprising the topic of Numbers. It will help students to have a better understanding of numbers. After solving the worksheet, students will have a better understanding of the following concepts: 1. Comparison of numbers as greater or lesser 2. Factors and multiples 3. Prime factors & Prime factorisation 4. HCF and LCM. I. Comparison of Numbers To compare any numbers, we must first check the number of digits in each number. The number with more digits is greater than the number with lesser digits. For example, let’s compare 23 & 458. We can see that 23 has 2 digits while 458 has 3. Therefore, 458 becomes the greater number since it has a larger number of digits than 23. With numbers having the same number of digits, we need to compare the digits from the left most place until we come across unequal digits. Then, we identify the greater of the unequal digits and identify the greater numbers.
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For example, let’s compare 1,469 and 1,463. Since the number of digits in both numbers are the same (that is 4), we must compare the digits from the left. Now 1, 4 and 6 are common among both numbers from the left. The unequal digits are 9 & 3 and since 9 is the greater number of the two, 1,469 is greater than 1,463. II. Factors & Multiples To understand factors & multiples, we must first know the concept of divisibility. Make sure to practise your knowledge of division at Takshila Learning. II.I Factors Now, if a number (dividend) is exactly divided by any number (divisor), the divisor is a factor of that dividend. For example, when we divide 100 (dividend) by 5 (divisor), it leaves no remainder and divides completely with 20 being the quotient. Thus we can say that 5 is a factor. If you notice carefully, even 20 is a factor because even it can divide 100 completely, leaving no remainder and quotient as 5. Thus we can say that for any number which is divided into another number and leaves no remainder, then both the divisor and the quotient is a factor of the dividend. To put it another way, When a number is considered to be a factor of another number, it means that the first number must entirely divide the second number, leaving no remainder. Now a fun thing to notice here! Each number has 1 as a common component since we can divide all numbers by 1. Therefore, 1 is a factor for all numbers. Another fun thing to notice is that each number is a factor of itself since every number will divide itself completely. For example, 20 is divisible by 20. Therefore, 20 is a factor of itself! Similarly, when we divide 30 by 5, it leaves no remainder and the quotient becomes 6. Thus we can say that 5, 30 and 1 are factors of 30. II.II Multiples A multiple of a number is the result of multiplying a given integer by another natural number. For example, multiples of 2 are 2 (2X1), 4 (2X2), 6 (2X3), 8 (2X4), etc. A quick tip to keep in mind is that whenever we need to calculate multiples, we can simply come up with the table of those particular numbers and calculate multiples. III. Prime Factors & Prime Factorisation III.I Prime Factors
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Every prime number that is a factor of a number is called a prime factor. For example, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30 since all of these numbers divide 30 completely. Now the prime factors out of these factors are 2, 3, and 5 since these are the only numbers that are prime numbers. III.II Prime Factorisation Prime factorization is a method of expressing a number as a product of its prime factors. To do so, we simply break down numbers as products of smaller factors until we can come down to only prime numbers. For example, let’s see the prime factorisation of 12. We first break down 12 as a product of 2 and 6. Then we can see that 6 can be broken down further as a product of prime numbers 2 & 3. Therefore, the prime factorisation of 12 is the product of the numbers in circles, that is, 2X2X3. IV. HCF & LCM III.I Highest Common Factor (HCF) The HCF or the greatest common factor is the common factor of 2 numbers that is the greatest among all other factors. For example, let’s calculate the HCF of 10 & 20. First we will list all the factors of both numbers –
prime factorisation of 12
10 – 1, 2, 5, 10 20 – 1, 2, 5, 10, 20 Since, 1, 2, 5 and 10 are the common factors of both these numbers and 10 is the highest among them, 10 becomes the HCF or the GCF for 10 & 20. III.II Lowest Common Multiple (LCM) The LCM is the common multiple of 2 numbers that is the lowest among all other multiples. For example, let’s calculate the LCM of 5 & 6. Here, we calculate the first few multiples of 5 & 6 and notice that 30 is the first common multiple of the two numbers. If we keep continuing to find common multiples further, they will all be greater than 30. Therefore, 30 is the LOWEST Common Multiple. Now that we have all these concepts in mind, let’s practise a few questions! 1. Find the greatest and the smallest of the following numbers a. 654, 54684,18,175,169
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Ans. Greatest ___
Smallest ___
b. 84, 846, 841, 86,158 Ans. Greatest ___
Smallest ___
c. 84, 78, 45, 97, 85 Ans. Greatest ___
Smallest ___
d. 564, 846, 484, 847, 864 Ans. Greatest ___
Smallest ___
LCM of 5 & 6
e. 7845, 658, 621, 4646 Ans. Greatest ___
Smallest ___
f. 846, 484, 571, 961, 546 Ans. Greatest ___
Smallest ___
g. 254, 213, 5431, 458,1561 Ans. Greatest ___
Smallest ___
h. 78, 45, 96, 54, 82, 12, 23 Ans. Greatest ___
Smallest ___
i. 78,154,16,151, 254, 51,15 Ans. Greatest ___
Smallest ___
j. 784, 516, 851, 24, 568, 546 Ans. Greatest ___
Smallest ___
2. Write the factors of the following numbers a. 32 b. 45 c. 65 d. 200 e. 99 f. 121
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g. 79 h. 45 i. 22 j. 23 3. Write first three multiples of each of the following numbers a. 5 – b. 7 – c. 9 – d. 12 – e. 15 – f. 13 – g. 78 – h. 100 – i. 200 – j. 10 – 4. Which number is the factor of every number? 5. Write all the prime numbers between the following: a. 10 – 20 – b. 20 – 30c. 30 – 40 – d. 40 – 50 – e. 50 – 60 – Download playing with numbers class 6 worksheet
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playing with numbers class 6 worksheet
6. Write the prime factorization of the following numbers: a. 84 – b. 28 – c. 65 –
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d. 37 – e. 89 – f. 99 – g. 44 – h. 121 – i. 45 – j. 22 – 7. Fill the table with ‘Yes’, wherever applicable. The first number has been solved as an example. Number
Divisible by 2
152
Yes
3
4 Yes
5
6
7
8
9
Yes
84 657 23 75 12 165 85 99 100 8. Find the HCF of the following numbers: a. 21, 24 – b. 15, 45 – c. 78, 13 – d. 91, 13 – e. 23, 97 –
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9. Find the LCM of the following numbers: a. 45, 84 – b. 84, 75 – c. 25, 15 – d. 75, 5 – e. 99, 3 – Download grade 6 maths worksheet playing with numbers
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class 6 maths worksheet on numbers
ANSWERS 1. Find the greatest and the smallest of the following numbers: a. 654, 54684, 18, 175,169 Ans. Greatest – 54684, Smallest – 18
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b. 84, 846, 841, 86,158 Ans. Greatest – 846, Smallest – 84 c. 84, 78, 45, 97, 85 Ans. Greatest – 45, Smallest – 97 d. 564, 846, 484, 847, 864 Ans. Greatest – 484, smallest – 864 e. 7845, 658, 621, 4646 Ans. Greatest – 7845, Smallest – 621 f. 846, 484, 571, 961, 546 Ans. Greatest – 961, Smallest – 484 g. 254, 213, 5431, 458, 1561 Ans. Greatest – 5431, Smallest – 213 h. 78, 45, 96, 54, 82, 12, 23 Ans. Greatest – 96, Smallest – 12 i. 78, 154, 16, 151, 254, 51,15 Ans. Greatest – 254, Smallest – 15 j. 784, 516, 851, 24, 568, 546 Ans. Greatest – 784, Smallest – 24 2. Write the factors of the following numbers: a. 32 – 1, 2, 4, 8, 16, 32 b. 45 – 1, 3, 5, 9, 15, 45 c. 65 – 1, 5, 13, 65 d. 200 – 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200 e. 99 – 1, 3, 9, 11, 33, 99 f. 121 – 1, 11, 121 g. 79 – 1, 79
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h. 45 – 1, 3, 5, 9, 15, 45 i. 22 – 1, 2, 11, 22 j. 23 – 1, 23 3. Write first three multiples of each of the following numbers: a. 5 – 5, 10, 15 b. 7 – 7, 14, 21 c. 9 – 9, 18, 27 d. 12 – 12, 24, 36 e. 15 – 15, 30, 45 f. 13 – 13, 26, 39 g. 78 – 78, 156, 234 h. 100 – 100, 200, 300 i. 200 – 200, 400, 600 j. 10 – 10, 20, 30 4. Which number is the factor of every number? Ans. 1 5. Write all the prime numbers between the following: a. 10 – 20: 11, 13, 17, and 19. b. 20 – 30: 23 and 29. c. 30 – 40: 31 and 37. d. 40 – 50: 41, 43, and 47. e. 50 – 60: 53, 57 and 59. 6. Write the prime factorization of the following numbers: a. 84 – 2 x 2 x 3 x 7. b. 28 – 2 x 2 x 7. c. 65 – 5 x 13.
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d. 37 – It is a prime number. Therefore, 37×1. e. 89 – It is a prime number. Therefore, 89×1. f. 99 – 3 x 3 x 11. g. 44 – 2 x 2 x 11. h. 121 – 11 x 11. i. 45 – 3 x 3 x 5. j. 22 – 2 x 7. Fill the table with yes, the first one is done as an example. Number
Divisible by 2
152
Yes
84
Yes
657
3
4
5
6
7
Yes Yes
8
9
Yes
Yes
Yes
Yes
Yes Yes
23 75 12
Yes Yes
165
Yes Yes
85
Yes Yes
Yes Yes Yes
99
Yes
Yes
100
Yes
Yes
8. Find the HCF of the following numbers: a. 21, 24 – 3 b. 15, 45 – 15 c. 78, 13 – 13 d. 91, 13 – 13 e. 23,97 – 1 9. Find the LCM of the following numbers: 12/13
a. 45, 84- 1260 b. 84, 75 – 2100 c. 25,15 – 75 d. 75, 5 – 75 e. 99, 3 – 99 Related grade 6 Maths Important Questions for CBSE Class 6 Maths Prepare NCERT Class 6 Maths with our Online Tuition Classes for 6th and Interactive Live Online Classes Here at Takshila Learning online live class platform, we provide Online Classes for School from Preschool to Class 12 for all subjects. We provide the best online tuition classes for Class 10 and other classes that comprise Video lectures and Online Live Classes that will help students to grasp concepts easily. We also provide Worksheets & Assignments, Doubt sessions, Free Encyclopedia, NCERT Solutions for Class 6 to 12, and Exam Guru to monitor your progress, i.e., subject-wise and topic-wise. So now Enjoy E-Learning with Takshila Learning. Learning is fun now! Subscribe to our social channel. Enroll today & Get Free Demo Class!
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