Largest Number Which Divides 70 and 125 Leaving Given Remainders

Video Explanation

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Solution

Question: The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is:

(a) 13    (b) 65    (c) 875    (d) 1750

Step 1: Subtract the Remainders

70 − 5 = 65

125 − 8 = 117

Step 2: Find the HCF of the New Numbers

65 = 5 × 13

117 = 9 × 13

HCF(65, 117) = 13

Final Answer

✔ The largest required number is 13.

✔ Correct option: (a) 13

Conclusion

Thus, the largest number that divides 70 and 125 leaving remainders 5 and 8 respectively is 13.