Question : What is the greatest number which divides 784 and 857 and leaves the remainder 4 and 2, respectively?
Option 1: 3
Option 2: 5
Option 3: 30
Option 4: 15
Correct Answer: 15
Solution :
The number that divides 784 and leaves a remainder of 4 = 784 – 4 = 780
The number that divides 857 and leaves a remainder of 2 = 857 – 2 = 855
The greatest number that divides both 780 and 855 is their highest common factor (HCF).
Factors of 780 = 2, 3, 5, 13
Factors of 885 = 3, 3, 5, 9
The HCF of 780 and 855 = 3 × 5 = 15
Hence, the correct answer is 15.
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