Answer :

Given: - 249 and 309 are numbers to be divided by some number that leaves 9 as the remainder

Let that some number i.e divisor is x

When x divides 249 and 309 leaves remainder 9

Then, to completely divides them it should be reduced by 9

Therefore 249 – 9 = 240 and 309 – 9 = 300

Now as x divides both the number (i.e 240 and 300) therefore we have to find a highest common factor of 240 and 300

Hence,

Factors of 240 = 2 × 2 × 2 × 2 × 3 × 5

Factors of 300 = 2 × 2 × 3 × 5 × 5

Highest common factors are = 2 × 2 × 3 × 5

x = 60

So 60 is the number which divides both 249 and 309 with 9 as remainder.

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