Question

Consider the number $N=10800$.
Number of ordered triplets ( $x,y,z)$ of positive integers such that $xyz=N$, is

• A. 900
• B. 1770
• C. 3540
• D. None

Answer 1

Answer: (A)

(ii) $10800=2^4\cdot 3^3\cdot 5^2$
Consider a, b, c as beggars and powers on 2,3 and 5 as identical objects to be distributed in a, b, c. Hence number of ways is

NOTE: ${}^{60}{C}_2$ is wrong because if we take two divisiors as $2^3\times 3^3\times 5^2$ and $2^4\times 3^3\times 5^2$ then their product will exceed the number 10800 .