Question

The number of factors (excluding 1 & the expression itself) of the product of $a^7{b}^4{c}^{3}def$ where $a,b,c,d,e,f$ are all prime numbers is

• A. 634
• B. 1872
• C. 1278
• D. 2078

Answer 1

Answer: (C)

1278

To find Number of factors of the product $a^7{b}^4{c}^{3}def$
If we have to find the number of factors of the product
$=x^a{y}^b{z}^c$
Then, Number of factors
$=(a+1)(b+1)(c+1)-2$
Therefore, Number of factors of the product $a^7{b}^4{c}^{3}def$
$=(7+1)(4+1)(3+1)(1+1)(1+1)(1+1)-2$
$=1280-2$
$=1278$
Hence, Option C is correct.