Question

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

Answer 1

If the number divides 285, it leaves remainder 9.
So 285 - 9 = 276 is a multiple of the number

If the number divides 1249, it leaves remainder 7.
So 1249 - 7 = 1242 is a multiple of the number

To find the greatest such number, we need to find the HCF of 276 and 1242.

276 = 2×2×3×23

1242 = 2×3×3×3×23

HCF = 2×3×23 = 138


Thus the greatest number which divides 285 and 1249 leaving remainders 9 and 7 is 138.