The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively. Is


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

5
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