## Maharashtra State Board Class 6 Maths Solutions 9 HCF-LCM Practice Set 23

Question 1.

Write all the factors of the given numbers and list their common factors:

i. 12, 16

ii. 21, 24

iii. 25, 30

iv. 24, 25

v. 56, 72

Solution:

i. Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 16 = 1, 2, 4, 8, 16

∴ Common factors of 12 and 16 = 1, 2, 4

ii. Factors of 21 = 1, 3, 7, 21

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

∴ Common factors of 21 and 24 = 1, 3

iii. Factors of 25 = 1, 5, 25

Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30

∴ Common factors of 25 and 30 = 1, 5

iv. Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

Factors of 25 = 1,5, 25

∴ Common factor of 24 and 25 = 1

v. Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56

Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

∴ Common factors of 56 and 72 = 1, 2, 4, 8

**Maharashtra Board Class 6 Maths Chapter 9 HCF-LCM Practice Set 23 Intext Questions and Activities**

Question 1.

In the empty boxes, write the proper words: dividend, divisor, quotient, remainder. (Textbook pg. no. 46)

Solution:

When we divide 36 by 4, the remainder is zero. Therefore, 4 is a factor of 36 and 36 is a multiple of 4. But, when we divide 65 by 9, the remainder is not zero. Therefore, 9 is not a factor of 65. Also, 65 is not a multiple of 9.

Question 2.

Write all the factors of the numbers 36 and 48. Also, list their common factors. (Textbook pg. no. 46)

Solution:

36 = 1 × 36

= 2 × 18

= 3 × 12

= 4 × 9

= 6 × 6

48 = 1 × 48

= 2 × 24

= 3 × 16

= 4 × 12

= 6 × 8

∴ Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Common factors of 36 and 48: [1] ,[2], [3], [4], [6], [12]