Question

By Euclid division algorithm find HCF of 135 and 125.​

Answer 1

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Euclids Divison Algorithm.

According to this Euclids Division algorithm or lemma.

" FOR AN TWO INTEGERS WE HAVE "a" AND "b" THEIR EXIST AN UNIQUE INTEGERS "q" and "r" satisfying the condition a = bq+r where,

0 less than r less than b

So using this we can find the HCF

given :

find the HCF of 135 and 125.

start with the greatest number.

135 = 125 X 1 + 10 ----> this in the form of a= bq+r

similarly in the place of a we have to write b value and in place of b we have to write the r value

so, 125 = 10 × 12 + 5

10 = 5 X 2 + 0

we have to do this untill the r becomes zero (0).

when the r becomes 0 the b value will become the HCF value.

so, here

The HCF of 135 and 125 is 5.

Hope this is useful...