Question

Find H.C.F of 320 and 1055 using Euclid’s Division Algorithm

Answer 1

Answer:

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Answer 2

$\underline { \blue { Euclid's \: division \: Algorithm: }}$

Given positive integers 'a' and 'b' , there exist unique pair of integers 'q' and 'r' satisfying

a = bq + r , 0 ≤ r < b .

$Given \: two \: numbers \: 320 \:and \: 1055.$

When 1055 is divided by 320 , the remainder is 95 we get

1055 = 320 × 3 + 95

Now, Consider division of 320 with Remainder 95 and apply the division lemma to get

320 = 95 × 3 + 35

Repeat the process until the the Remainder become zero.

95 = 35 × 2 + 25

=> 35 = 25 × 1 + 10

=> 25 = 10 × 2 + 5

=> 10 = 5 × 2 + 0

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

Since , the divisor at this stage is 5 .

Therefore.,

$\red { H.C.F \:of \: 320 \:and \: 1055 } \green { = 5 }$

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