Question

answer this question
use Euclid's division algorithm to find the HCF of 10524 and 12752.

Answer 1

HCF of 10524 and 12752 by Euclid's division algorithm is 4.

Answer 2

HCF of 10524 and 12752 is 4

Given Numbers:  

10524 and 12752

To find:

HCF of 10524 and 12752 by using Euclid's division algorithm

Solution:

From Euclid's division lemma,

if b < a and a divided by b ⇒ a = b × quotient + Remainder

Here given number are 10524, 12752 and 10524 < 12752

Divide 12752 by 10524

⇒  12752 = 10524 × 1 + 10524  [Here Remainder is not zero ]

Now divide  10524 by 2228

⇒  10524 =  2228 × 4 + 1612   [ Here Remainder is not zero ]

Now divide 2228 by 1612

⇒  2228 = 1612 × 1 + 616       [ here Remainder is not zero]

Continue this until we get zero remainder

Now divide 1612 by  616

⇒  1612 = 616 × 2 + 380         [ here Remainder is not zero]

Now divide 616 by 380      

⇒ 616 = 380 × 1 + 236            here remainder is not zero

Now divide 380 by 236          

⇒ 380 = 236 × 1 + 144           [ here Remainder is not zero]

Now divide  236 by 144  

⇒  236 = 144 × 1 + 92            [ here Remainder is not zero]

Now divide 144 by 92  

⇒  144 = 92 × 1 + 52             [ here Remainder is not zero]

Now divide  92 by 52  

⇒  92 = 52 × 1 + 40             [ here Remainder is not zero]  

Now divide  52 by 40

⇒  52 = 40 × 1 + 12              [ here Remainder is not zero]  

Now divide  40 by 12

⇒  40 = 12 × 3 + 4                  [ here Remainder is not zero]

Now divide  12 by 4  

⇒  12 = 4 × 3 + 0                  [ here Remainder is zero]

As there is 0 remainder,

So we can conclude that  4 is the HCF (10524, 12752).

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