Methods of finding HCF

1.	Methods of finding HCF
Answer» (i) Prime Factorization : Express each of the given numbers as the product of their prime factors. The HCF of the given numbers is the product of the least powers of common factors. 24 = 2³ × 3, 32 = 2⁵ ⇒ HCF (24, 32) = 2³ = 8. (ii) Continued Division Method : Divide the larger number by the smaller number. If the remainder is zero, the divisor is the HCF, otherwise divide the previous divisor by the remainder last obtained. Repeat this until the remainder becomes zero. To find the HCF of more than two numbers, first find the HCF of any two numbers and then find the HCF of the result and the third number and so on. The final HCF is the required HCF. Note : The HCF of two co-prime numbers is 1, as they have no factors in common.

Answer»

(i) Prime Factorization : Express each of the given numbers as the product of their prime factors. The HCF of the given numbers is the product of the least powers of common factors.

24 = 2³ × 3, 32 = 2⁵ ⇒ HCF (24, 32) = 2³ = 8.

(ii) Continued Division Method : Divide the larger number by the smaller number. If the remainder is zero, the divisor is the HCF, otherwise divide the previous divisor by the remainder last obtained. Repeat this until the remainder becomes zero.

To find the HCF of more than two numbers, first find the HCF of any two numbers and then find the HCF of the result and the third number and so on. The final HCF is the required HCF.

Note : The HCF of two co-prime numbers is 1, as they have no factors in common.

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