Question

Find the largest number that divides 59 and 54 leaving remainders 3 and 5 respectively

Answer 1

First we will subtract 3 and 5 from 59 and 54 recpectively.
Now, we have 59 − 3 = 56 and 54 − 5 = 49
56 = 2 × 2 × 2 × 7 = 2³ × 7¹
49 = 7 × 7 = 7²
HCF of 56 and 49 = 7¹ = 7
Hence, the largest number that divides 59 and 54 leaving remainders 3 and 5 respectively is 7.