Question

Find the total number of factors of 4160___.

• A. 28
• B. 33
• C. 32
• D. 21

Answer 1

The correct option is A 28

$Theprimefactorsin\exp onentialformof$
$4160=2^6\times 5^1\times {13}^1$
$equation\text{for determining the number of factors}$
$\text{d}\left(n\right)=(a+1)(b+1)(c+1)$
$whered\left(n\right)isequal\text{to number of factors of the number}$
$\text{a,b,c are equal to te exponents of the prime factorization}$
$\text{d}\left(4160\right)=2^6\times 5^1\times {13}^1$
$=(6+1)(1+1)(1+1)$
$=7\times 2\times 2$
$=28$