Question

$P = 441 \times 484 \times 529 \times 576 \times 625$. The total number of factors are

• A. $607$
• B. $5706$
• C. $1024$
• D. $6075$

Answer 1

Answer: (D)

$6075$

$p=(21{)}^2\times (22{)}^2\times (23{)}^2\times (24{)}^2\times (25{)}^2$
$=(3\times 7{)}^2\times (2\times 11{)}^2\times (23{)}^2\times (2^3\times 3{)}^2\times (5^2{)}^2$
$=3^2\times 7^2\times 2^2\times {11}^2\times {23}^2\times 2^6\times 3^2\times 5^4$
$=2^8\times 3^4\times 5^4\times 7^2\times {11}^2\times {23}^2$
Total number of factors
$(8+1)\times (4+1)\times (4+1)\times (2+1)\times (2+1)\times (2+1)$
$=9\times 5\times 5\times 3\times 3\times 3=6075$