Question

Using euclid division algorithm to find hcf of 960 and 1575

Answer 1

Hi,

Euclid's division algorithm:

Given positive integers a and b , there

exist whole numbers q and r satisfying

a = bq + r , 0 < r < b

_

According to the problem given ,

Applying Ecuclid's division lemma to 960,

and 1575, we get

1575 = 960 × 1

960 = 615 ×1 + 270

615 = 270 × 1 + 75

270 = 75 × 3 + 45

75 = 45 × 1 + 30

45 = 30 × 1 + 15

30 = 15 × 2 + 0

Notice that the remainder has become zero,

and we cannot proceed anybfurther.

We claim that the HCF of 960 and 1575 is the

divisor at this stage , i.e . 15.

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