Question

Find the largest nos which divides 70 and 125 leaving remainder 5 and 8 respectively

Answer 1

Answer:

13

Explanation:

To find the greatest number which divides 70 and 125, we need to find the HCF (Highest Common Factor) of the two numbers subtracted by the remainders they leave when divided by the number we are asked to find.

⇒ 70 - 5 = 65

⇒ 125 - 8 = 117

Here, both 65 and 117 are divisible by the number we have to find. Therefore, the HCF (Highest common factor) of these two numbers will give us the answer required.

HCF(65, 117) = Largest number that divides 70 & 125.

By using Euclids Division Lemma;

a = bq + r.

117 = 65 × 1 + 52

65 = 52 × 1 + 13

52 = 13 × 4 + 0

HCF = 13

∴ The largest number which divides 70 and 125 leaving the remainder 5 and 8 respectively is 13.

Answer 2

Answer:

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