Question

find the greatest number which will devide 285 and 1249, leaving remainders 9 and 7 respectively.
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Answer 1

Answer:

The greatest number which divides 285 and 1249 leaving the remainder 9 and 7 respectively is 138.

Step-by-step explanation:

As we have to find the greatest number that divides the two, we need to Highest Common Factor (HCF) of the two numbers obtained after subtraction.

The numbers are given by the difference exactly divisible by the required number are given as :-

285 - 9 = 276

1249 - 7 = 1242

To find the greatest number that exactly divides these are given by their H.C.F :-

276 = 2 × 2 × 3 × 23

1242= 2 × 3 × 3 × 3 × 23

Common Numbers = 2 × 3 × 23

Highest Common Factor ( HCF) = 6 × 23

= 138

Therefore, the greatest number which divides 285 and 1249 leaving the remainder 9 and 7 respectively is 138.

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