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Find the sum of all the divisors of $2^{4} \times 3^{3}$ that are multiples of 6.

Competition practiceNumber System, HCF & LCM

A1170
B1210
C1240
D390

Step-by-Step Solution

A divisor that is a multiple of 6 has the form

2^{a} 3^{b}

with a ≥ 1 and

b

≥ 1. Sum =

(2 + 4 + 8 + 16) (3 + 9 + 27) = 30 \times 39 = 1170

.

Answer: A) 1170

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