Question

Find the hcf of 504 and 1188 using euclids algorithm

Answer 1

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Answer 2

Solution:

Euclid's Algorithm:

Let a and b be any two positive

integers .Then there exit two unique whole numbers q and r

such that

a = bq + r ,

0≤ r<b

Here , a is called the dividend,

b is called the divisor , q is called the quotient and r is called the remainder.

Now ,

Given 504 and 1188.

Start with the larger integer, that is 1188.

Apply the division algorithm to

504 and 1188

1188 = 504 × 2 + 180

Since , the remainder 180≠0, we apply the division algorithm to 180 and 504

504 = 180 × 2 + 144

similarly,

180 = 144 × 1 + 36

144 = 36 + 4 + 0

The remainder has now become zero , so our procedure stops.

Since , the divisor at this stage

is 36 ,

the HCF of 504 and 1188

is 36.

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