Since, it is given that 5 and 8 are the remainders of 70 and 125 respectively. On subtracting these remainders from the numbers we get 65 = (70-5) and 117 = (125-8), which is divisible by the required number.

Now, required number = HCF (65,117) [for the largest number]

According to Euclid’s division algorithm,

b = a × q + r, 0 ≤ r < a [∴dividend = divisor × quotient + remainder]

⇒ 117 = 65 × 1 + 52

⇒ 65 = 52 × 1 + 13

⇒ 52 = 13 × 4 + 0

⇒ HCF = 13

Hence, 13 is the largest number which divides 70 and 125, leaving remainders 5 and 8