Question

Find the HCF of each of the following numbers using prime factorisation. (a) 35, 420, 350 (b) 28, 42, 98​

Answer 1

Answer:

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Step-by-step explanation:

(i) 18,27,36

The three numbers can be represented as the product of their prime factors, as 3

2

×2, 3

3

and 3

2

×2

2

respectively.

The product of the lowest powers of the common factors among the three numbers is 2

1

×3

2

∴ HCF=2×3

2

=18

(ii)106,159,165

The three numbers can be represented as the product of their prime factors, as 2×53,3×53 and 5×53 respectively.

The product of the lowest powers of the common factors among the three numbers is 53

1

∴ HCF=53

(iii)10,35,40

The three numbers can be represented as the product of their prime factors, as 5×2,5×7, and 2

3

×5 respectively.

The product of the lowest powers of the common factors among the three numbers is 5

1

∴ HCF=5

(iv)32,64,96,128

The three numbers can be represented as the product of their prime factors, as 2

5

,2

6

,2

5

×3 and 2

7

respectively.

The product of the lowest powers of the common factors among the three numbers is 2

5

∴ HCF=2

5

=32