Question

How many factors does 2000 have ?

• A. 10
• B. 15
• C. 20
• D. 25

Answer 1

The correct option is C

20

Let us look into the prime factorisation of 2000.
$2000=2\times 2\times 2\times 2\times 5\times 5\times 5$,

i.e. 2 occurs four times and 5 occurs three times
Thus, it has $(4+1)\times (3+1)$ number of factors in all.

$5\times 4=20$
$⟹$ 2000 has 20 factors in all.