# Class 6 Maths Playing With Numbers | Model Questions

**CLASS 6 MATHEMATICS | Playing With Numbers | Practice Problems**

1. Write all the factors of 27.

2. Write first five multiples of 8.

3. Express the following as the sum of two odd primes.

a) 28

b) 18

4. Using divisibility test, determine 2150 is divisible by 4 and by 8.

5. Using divisibility tests, determine which of the following numbers are divisible by 11.

a) 1783695

b) 80124

6. Using divisibility tests, determine 87512 is divisible by 6.

7. Find the common multiples of 3, 4 and 5 and find its LCM?

8. Find the common factors of 4, 8 and 10 and find its HCF?

9. Which of the following numbers are co prime?

a) 23, 42

b) 30, 45

10. Determine the greatest 2 digit number exactly divisible by 4, 8 and 12?

**ANSWERS:**

1. Factor pairs of 27 are 1 x 27, 3 x 9.

So factors of 27 are 1, 3, 9 and 27.

2. First five multiples of 8 are 8, 16, 24, 32, and 40.

3. a) 28 = 23 + 5

b) 18 = 11 + 7

4. A number with 3 or more digits is divisible by 4 if the number formed by its last two digits is divisible by 4.

Here the number is 2150.

Its last two digits are 50.

50 is not divisible by 4, therefore the number 2150 is not divisible by 4.

A number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8.

Here the number is 2150.

Its last three digits are 150.

150 is not divisible by 8, therefore the number 2150 is not divisible by 8.

5. a) 1783695

Sum at odd place = 5 + 6 +8 +1 = 20

Sum at even place = 9 + 3+7 = 19

Difference = 20- 19 = 1

Therefore 1783695 is not divisible by 11.

b) 80124

Sum at odd place = 4 + 1 + 8 = 13

Sum at even place = 2 + 0 = 2

Difference = 13 – 2 = 11

Therefore, 80124 is divisible by 11.

6. If a number is divisible by 2 and 3 both then it is divisible by 6 also.

Here the number is 87512.

Since it is an even number, it is divisible by 2.

Sum of the digits = 8 + 7 + 5+ 1+2 = 23, which is not a multiple of 3.

So it is not divisible by 3.

Therefore, 87512 is not divisible by 6.

7. Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60 ……..

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60……………………….

Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 ……………..

Common multiples are 60, 120, 180 ……………………

LCM = 60

8. Factors of 4 are 1, 2, and 4.

Factors of 8 are 1, 2, 4, and 8.

Factors of 10 are 1, 2, 5, and 10.

Common factors are 1 and 2.

HCF = 2

9. Two numbers having only 1 as a common factor are called co – prime numbers.

a) Factors of 23 are 1 and 23.

Factors of 42 are 1, 2, 3, 6, 7, 14, 21and 42.

But the common factor is 1.

Therefore 23 and 42 are co – prime.

b) Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.

Factors of 45 are 1, 3, 5, 9, 15 and 45.

Common factors are 1, 3, 5 and 15.

Therefore 30 and 45 are not co – prime.

10. Here we need to find the LCM of 4, 8 and 12.

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40………………..

Multiples of 8 are 8, 16, 24, 32, 40, 48……………..

Multiples o 12 are 12, 24, 36, 48, 60 ………………

Common Multiples are 24, 48, 72, 96, 120, 144 …………………………..

Therefore, the greatest two digit number which is exactly divisible by 4, 8 and 12 are 96.