Question

Which of the following does satisfy the following property?
A number which divides 542 and 128 and leaves a remainder 2 in both cases.

• A. 3
• B. 6
• C. 9
• D. 12

Answer 1

Answer: (A), (B), (C)

The correct options are
A

3

B

6

C

9

Suppose the number be $x$. Since it divides 542 and 128 leave a remainder 2, using the Euclid’s division algorithm for 542 and $x$, $542=ax+2$, where a is an integer. So, $ax=542–2=540$, i.e $x$ is a factor of 540. Similarly $x$ is a factor of (128 - 2).

The HCF of 542 – 2 = 540, 128 – 2 = 126 :
Step 1 : $540=126\times 4+36$
Step 2 : $126=36\times 3+18$
Step 3 : $36=18\times 2+0$

HCF is 18
3, 6, 9 are factors of 18 and therefore satisfy the given property. 12 is the only number which isn’t a factor.