Question

using Euclid's division algorithm,find hcf of 272 & 1040​

Answer 1

$\underline { \pink { Euclid's \: Division \: Algorithm :}}$

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

$\boxed{ \blue { a = bq + r , 0 \leq r < b }}$

$Given \: numbers \: 272 \:and \: 1040.$

When 1040 is divided by 272 ,the remainder is 224 we get

1040 = 272 × 3 + 224

Now consider division of 272 with remainder 224 and apply the division lemma to get

272 = 224 × 1 + 48

Continue the process

224 = 48 × 8 + 32

48 = 32 × 1 + 16

32 = 16 × 2 + 0

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

Since ,the divisor at this stage is 16 ,

Therefore.,

$\red{ HCF \:of \: 272 \:and \:1040 } \green {= 16}$

•••♪