Question

Which of the following does not 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

The correct option is D

12

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: $36=18\times 2+0$

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