Find the HCF of 56 and 88.

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HCF(56, 88) = 7

HCF(56, 88) = 8

HCF(56, 88) = 6

HCF(56, 88) = 9

answer is B.

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Detailed Solution

Given to define HCF of two positive integers and to find HCF(56, 88).
The highest common factor (HCF) for two or more numbers is the largest number that
divides them.
Euclid's Division Lemma states that if two positive integers a and b exist, then there must be unique values of q and r that satisfy the formula a= bq + r, where 0 ≤ r < b.
Apply Euclid’s division lemma on 56, 88

88 = 56 × 1 + 32

∵

remainder

≠ 0,

apply Euclid’s division lemma on divisor 56 and remainder 32

56 = 32 × 1 + 24

∵

remainder

≠ 0,

apply Euclid’s division lemma on divisor 32 and remainder 24

32 = 24 × 1 + 8

∵

remainder

≠ 0,

apply Euclid’s division lemma on divisor 24 and remainder 8

24 = 8 × 3 + 0

∴

remainder = 0.
Therefore, the highest common factor (HCF) for two or more numbers is the largest number that divides them and HCF(56, 88) = 8.
Hence the correct option is 2.

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