find the greatest number which divides  285 and 1249, leaving remainders 9 and 7 respectively?

 

Hi!
Here is the answer to your question.
 
Since on dividing 285 by the required number, the remainder is 9.
∴ 285 – 9 = 276 will be exactly divisible by the required number.
Similarly, 1249 – 7 = 1242 will be also exactly divisible by the required number.
∴The required number is HCF of 276 and 1242.
Prime factorization of 276 = 2×2×3×23
Prime factorization of 1242 = 2×3×3×3×23
HCF of 276 and 1242 = 2×3×23 = 138
Thus, the required greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively is 138.
 
Cheers!

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