Question

using Euclids algorithm, find the HCF of 960and1575

Answer 1

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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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