Question

Find the greatest number which divides 285 and 1249 leaving the remainder 9 and 7 respectively
A) 135
B) 136
C) 137
D) 138

Answer 1

Hint: When the required number divides the given numbers (285 and 1249), it leaves certain remainders, thus the difference between the two will provide us those numbers that are completely divisible by the required number.

Complete step-by-step answer:
As we have to find the greatest number that divides the two, we need to highest common factor (H.C.F) 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 X 2 X 3 X 23
1242 = 2 X 3 X 3 X 3 X 23
Common numbers = 2 X 3 X 23
Highest Common Factor (H.C.F) = 6 X 23
Highest Common Factor (H.C.F) = 138
Therefore, the greatest number which divides 285 and 1249 leaving the remainder 9 and 7 respectively is 138, option D).
So, the correct answer is “Option D”.

Note: A factor is a number that divides another number without leaving any remainder.
H.C.F of two numbers is the product of common prime factors between the two where a prime number is divisible only by 1 and itself.
H.C.F of the two numbers cannot be greater than either of them.
H.C.F can also be called G.C.F which stands for greatest common factor.