Question

Which is the greatest number that will divide 137, 182 and 422, leaving the remainder 2 in each case?

• A. 15
• B. 45
• C. 20
• D. 90

Answer 1

The correct option is A 15

Here, 137 – 2 =135, 182 – 2 = 180, 422 – 2 = 420
Therefore, the required number is the HCF of the numbers 135, 180, 420.
$135=3\times 3\times 3\times 5180=2\times 2\times 3\times 3\times 5420=2\times 2\times 3\times 5\times 7$
HCF of 135, 180 and $420=3\times 5=15$