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,
$65=13 \times 5$
$117=13 \times 3 \times 3$
$\therefore \mathrm{HCF}=13$
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