Question

The largest number which divides by 72 and 125,leaving remainders 7 and 8 respectively is​

Answer 1

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Answer 2

Concept:

Remainder: When we divide a number by another number and it is not completely divided then the leftover part is known as the remainder.

Given:

We have, 72 and 125 as divisors, and  7 and 8 as the remainders respectively.

Find:

We are asked to find the largest number.

Solution:

So,

To find the largest number,

Now,

Divisor = Dividend × Quotient + Remainder

So,

72 = Dividend × Quotient + 7

Let,

72 = x + 7

⇒ x = 65

And,

125 = Dividend × Quotient + 8

125 = y + 8

⇒ y = 117

Now,

Find HCF of 65 and 117,

65 = 13 × 5

117 = 3 × 3 × 13

So,

HCF(65, 117) = 13

Hence, the largest number is 13.

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