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Use euclid division algorithm to find …

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Use euclid division algorithm to find the largest number which divides 957 and 1280 leaving 5 in each case.
  • 1 answers

Sia ? 6 years, 6 months ago

Given numbers are 957 and 1280 and remainder is 5 in each case.Then , new numbers after subtracting remainders are 
957 –  5 = 952 and 1280 –  5 = 1275
Now, by using Euclid's Division lemma  , we get
1275 = (952  × 1) + 323
Here remainder = 323
So, on taking 952 as dividend and 323 as new divisor and then apply Euclid's Division lemma, we get
952 = (323  × 2) + 306
Again, remainder = 306.

So, on taking 323 as dividend and 306 as new divisor and then apply Euclid's Division lemma, we get
323 = (306  × 1) + 17
Again, remainder = 17.

So, on taking 306 as dividend and 17 as new divisor and then apply Euclid's Division lemma, we get
306 = (17  × 18) + 0
Here, remainder = 0.

Since, remainder has now become zero and the last divisor is 17.

Therefore, HCF of 952 and 1275 is 17.

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