Question

use euclids division algorithm to find hcf of 92690,7378,7161

Answer 1

By Euclid's division Lemma on 92690 and 7378
For every point of integers a and b there exist unique integer q and r such that a = bq + r  
 where 0 ≤  r < b 
 ​So here  and a > b
a = 92690 And b = 7378 ,So that
92690 = 7378  ×  13 + 4154
7378 = 4154  × 1 + 3224
4154 = 3224  × 1 + 930
3224 = 930  ×  3 +  434
934 = 434  × 2 + 62
434 = 62  ×  7 + 0
Here r = 0 So H.C.F. of ​92690 and 7378 is 62 
Now apply Euclid division lemma on 62 and 7161
Here a = 7161 and b = 62 ,So that a> b
7161 = 62 ​ ×  115 + 31
62 = 31 ​ ×   2  + 0
Here  r = 0 , So h.C.F. of ​62 and 7161 is 31 .
∴  H.C.F. of ​​92690 , 7378 ​and 7161  is = 31.

Answer 2

$92690 = 7378 \times 12 + 4154 \\ 7378 = 4154 \times 1 + 3224 \\ 4154 = 3224 \times 1 + 930 \\ 3224 = 930 \times 3 + 434 \\ 930 = 434 \times 2 + 62 \\ 434 = 62 \times 6 + 62 \\ 62 = 62 \times 1 = 0 \\ hcf \: = 62 \\ 7161 = 62 \times 115 + 31 \\ 62 = 31 \times 2 + 0 \\ hcf \: of \: these \: number \: is \: 31$