Question

1. If ‘a’ and ‘b’ are two positive integers such that a =14b. Find the HCF of ‘a’ and ‘b’​

Answer 1

Step-by-step explanation:

If a and b are the two +ve integers then

According to Euclid's division lemma

a=bq+r. where 0<=r<b

As a=14b then

14b=b×14+0

So the HCF is b.

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Answer 2

Given:-

• 'a' and 'b' are two positive Integers
• a = 14b

To Find:-

• The HCF of 'a' and 'b'

Concept:-

• Firstly let's understand the concept.'a' and 'b' are two known positive integers and a = 14b.We need to find the HCF of both 'a' and 'b'.

• Concept used is Euclid's Division Lemma.According to Euclid's Division Lemma,For any positive integer 'a' and 'b' a = bq + r and 0<=r<b.

Solution:-

'a' and 'b' are positive integers

a = 14b______(1)

a = b × 14 + 0____(2)

Substituting equation (1) in equation (2) we get!

14b = b × 14 + 0

14b = 14b

Therefore,

The HCF of 'a' and 'b' is b