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1.

If Pn means prime factors of n, find:(i) P6(ii) P24(iii) P50(iv) P42

Answer»

(i) F6 = 1, 2, 3, 6

P.F6 (Prime factor of 6) = 2 and 3.

(ii) F24 = 1, 2, 3, 4, 6, 8, 12, 24

P.F24 = 2 and 3.

(iii) F50 = 2, 5, 5

P.F50 = 2 and 5.

(iv) F42 = 1, 2, 3, 6, 7, 14, 21, 42

P.F42 = 2, 3 and 7.
Discussion
2.

Using the prime factor method, find the H.C.F. of:(i) 5 and 8(ii) 24 and 49(iii) 40, 60 and 80(iv) 48, 84 and 88(v) 12, 16 and 28

Answer»

(i) Prime factor of 5 = 5

Prime factor of 8 = 2 x 2 x 2

No common prime factor

H.C.F. of 5 and 8 = 1

(as both the number are co-prime)

(ii) Prime factor of 24 = 2 x 2 x 2 x 3

Prime factor of 49 = 7 x 7

No common prime factor, number are co-prime.

H.C.F. of 24 and 49 = 1.

(iii) Prime factor of 40 = 2 x 2 x 2 x 5

Prime factor of 60 = 2 x 2 x 3 x 5

Prime factor of 80 = 2 x 2 x 2 x 2 x 5

Common prime factor = 2 x 2 x 5

H.C.F. of 40, 60 and 80 = 2 x 2 x 5 = 20

(iv) Prime factor of 48 = 2 x 2 x 2 x 2 x 3

Prime factor of 84 = 2 x 2 x 3 x 7

Prime factor of 88 = 2 x 2 x 2 x 11

Common prime factor of 48, 84 and 88 = 2 x 2

H.C.F. of 48, 84 and 88 = 2 x 2 = 4

(v) Prime factor of 12 = 2 x 2 x 3

Prime factor of 16 = 2 x 2 x 2 x 2

Prime factor of 28 = 2 x 2 x 7

Common prime factor between 12, 16 and 28 = 2 x 2

H.C.F. of 12, 16 and 28 = 2 x 2 = 4
Discussion
3.

The product of two numbers is 432 and their L.C.M. is 72. Find their H.C.F.

Answer»

Product of two numbers = Product of their L.C.M. and H.C.F.

Here, product of two number = 432

L.C.M. = 72

H.C.F. = 432/72 = 6
Discussion
4.

Write all the factors of : (i) 15 (ii) 55 (iii) 48 (iv) 36 (v) 84

Answer»

(i) Factors of 15 = F15 = 1, 3, 5 and 15 

(ii) Factors of 55 = F55 = 1, 5, 11 and 55 

(iii) Factors of 48 = F48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 

(iv) Factors of 36 = F56 = 1, 2, 3, 4, 6, 9, 12, 18 and 36. 

(v) Factors of 84 = F84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84
Discussion
5.

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

Answer»

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
Discussion
6.

Find the HCF of the following numbers.i. 45, 30 ii. 16, 48 iii. 39, 25 iv. 49, 56 v. 120, 144

Answer»

i. Factors of 45 = 1, 3, 5, 9,15, 45 

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

∴ HCF of 45 and 30 = 15

ii. Factors of 16 = 1, 2, 4, 8, 16 

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

∴ HCF of 16 and 48 = 16

iii. Factors of 39 = 1, 3, 13, 39 

Factors of 25 = 1, 5, 25 

∴ HCF of 39 and 25 = 1

iv. Factors of 49 = 1, 7, 49 

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

∴ HCF of 49 and 56 = 7

v. Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 

Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 

∴ HCF of 120 and 144 = 24
Discussion