Question

use euclid's division algorithm to find the largest number which divides 957 and 1280 leaving remainder 5 in each case

Answer 1

first subtract 5 from 957 and 1280

957 – 5 = 952

1280 – 5 = 1275

Now using Euclid's Division Algorithm we will find the HCF of 952 and 1275

1275 = 952 ×1+323

952 = 323 × 2 + 306

323 = 306 × 1+ 17

306 = 17 × 18 + 0

The largest no. that divides 957 and 1280 leaving a reminder 5 is 17

Answer 2

Answer:

17

Step-by-step explanation:

The largest number which divides the given number 957 and 1280 gives 5 as the remainder is 17.

Solution:

Let the largest number be x.  

Given, when 957 is divided by x, it leaves remainder 5

Thus, (957-5) is divisible by x, i.e. 952 is divisible by x.  

Given, when 1280 is divided by x, it leaves remainder 5

Thus, (1280-5) is divisible by x, i.e. 1275 is divisible by x.  

Hence, x = H. C. F. of 952, 1275.  

Factors of 952 = 2 x 2 x 2 x 7 x 17

Factors of 1275 = 3 x 5 x 5 x 17

Thus, the H. C. F. of 952, 1276 = 17.  

Thus, the largest number which divides the given number 957 and 1280 gives 5 as the remainder is 17.