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

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The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is 13. Explanation: We have to find the largest number which divides 70 and 125 Leaving remainders 5 and 8 This can be also written as, To find the largest number which exactly divides (70 – 5) and (125 – 8) The largest number that divides 65 and 117 is also the Highest Common Factor of 65 and 117 Therefore, the required number is the HCF of 65 and 117 Factors of 65 = 1, 5, 13, 65 Factors of 117 = 1, 3, 9, 13, 39, 117 Common Factors = 1, 13 Highest Common factor (HCF) = 13 i.e., The largest number which divides 70 and 125 Leaving remainders 5 and 8, respectively = 13

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