Q2 of 15 Page 26

Find the greatest number that divides 249 and 309 leaving remainder 9?

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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