What is the largest number that divides 70 and 125,

Question:

What is the largest number that divides 70 and 125, leaving remainders 5 and 8 respectively?

(a) 13
(b) 9
(c) 3
(d) 585

Solution:

(a) 13

We know the required number divides 65 (70 − 5) and 117 (125 − 8).
∴ Required number = HCF (65, 117)
we know,

$65=13 \times 5$

$117=13 \times 3 \times 3$

$\therefore \mathrm{HCF}=13$