Find the largest number which divides 70 and 125 leaving remainders 5 and 8 respectively

We know the required number divides 65 (70 – 5) and 117 (125 – 8)

∴ Required number = HCF (65, 117)

We know, 65 = 13 × 5 117 = 13 × 3 × 3

∴ HCF = 13

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