Find the HCF of 70 and 30.

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HCF(70, 30) = 8

HCF(70, 30) = 9

HCF(70, 30) = 11

HCF(70, 30) = 10

answer is D.

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Detailed Solution

Given to define HCF of two positive integers and to find HCF(70, 30).
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 70, 30

70 = 30 × 2 + 10

∵

remainder

≠ 0,

apply Euclid’s division lemma on divisor 30 and remainder 10

30 = 10 × 3 + 0

∴

remainder = 0.
Therefore, the highest common factor (HCF) for two or more numbers is the largest number that divides them and HCF(70, 30) = 10.
Hence the correct option is 4.

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