Question

Using Euclid lemna find the HCF of 615 and 154

Answer 1

Let a=615 and b=154
By Euclids Division Lemma,
      a=bq+r     
    615 = 154*3+153
    154 = 153*1+1
    153=1*153+0
Therfore the HCF of 615 and 154 is 1

Answer 2

Using Euclid Lemna the HCF of 615 and 154 is 1.

Given: Two numbers are 615 and 154.

To find: The HCF of 615 and 154

Solution :

Step 1: Applying Euclid's division lemma, a = bq + r in 615 and 154.

Here, 615 > 154.

Let a = 615  and b = 154

615 = 154 × 3 + 153

Here, remainder = 153  ≠ 0, so take the new dividend as 154 and the new divisor as 153.

Step 2 : Applying Euclid's division lemma, a = bq + r in 154 and 153.

Let a = 154 and b = 153

154 = 153 × 1 + 1

Here, remainder = 1  ≠ 0, so take the new dividend as 153 and the new divisor as 1.

Step 3 : Applying Euclid's division lemma, a = bq + r in 153 and 1.

Let a = 153 and b = 1

153 = 1 ×  153 + 0

Here, remainder is zero and divisor is 1.

Hence ,H.C.F. of 615 and 154 is 1.

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