Question

Find the largest number that divides 220 313 and 716 leaving remainder 3 in each case​

Answer 1

Given:

Find the largest number that divides 220 313 and 716 leaving the remainder 3 in each case​.

To find:

The required number

Solution:

It is that the remainder is 3.

Subtract 3:

220 - 3 = 217

313 - 3 = 310

716 - 3 = 713

HCF of 217, 310, and 713 using prime factorisation:

217 = 7 × 31

310 = 2 × 5 × 31

713 = 23 × 31

HCF of 217, 310, and 713 = 31

So, the required number is 31

Hence, 31 is the largest number that divides 220 313 and 716 leaving the remainder 3 in each case​.