Find the greatest number which divides 108,124 and 156, leaving the same remainder.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 16
The given numbers are 108, 124, and 156.
After dividing by the greatest number, the remainder in each case is the same.
The greatest number that will divide a, b, and c and leaving the same remainder in each case is given by the HCF of |a - b|, |b - c|, and |c - a|.
ATQ -
|108 - 124| = |-16| = 16
|124 - 156| = |-32| = 32
|156 - 108| = 48
Prime factors of 16 = 2 × 2 × 2 × 2
Prime factors of 32 = 2 × 2 × 2 × 2 × 2
Prime factors of 48 = 2 × 2 × 2 × 2 × 3
HCF of 16, 32, and 48 = 2 × 2 × 2 × 2 = 16