Question

How many factors does a product of four distinct primes have?

• A. 5
• B. 10
• C. 4
• D. 16

Answer 1

The correct option is D 16

Let $a,b,c$ and $d$ be four distinct primes.
Then the factors of $a\times b\times c\times d$ are:
1,
$a$, $b$, $c$, $d$ (One prime at a time),
$a\times b$, $a\times c$, $a\times d$, $b\times c$, $b\times d$, $c\times d$ (Two primes at a time),
$a\times b\times c$, $a\times b\times d$, $a\times c\times d$, $b\times c\times d$ (Three primes at a time), and
$a\times b\times c\times d$ (All four primes) - 16 in total.