Question

The number of factors of $2^1{.3}^2{.5}^3$ are

• A. 12
• B. 24
• C. 36
• D. 48

Answer 1

The correct option is B

24

When a number is expressed as a product of its primes as shown,

$N=p^a{q}^b{r}^c$

The total number of factors is given by = (a +1)(b +1)(c +1)

N = $2^1\times 3^2\times 5^3$

Therefore, the total number of factors = (1 +1)(2+1)(3 +1) = 24.​