Question

$2.$ For $n=1451520$
$\left(i\right)$ Find the total number of divisors.
$\left(ii\right)$ Find the number of even divsors.
$\left(iii\right)$ Find the number of divisors of the form $2m+1$ where $m$ is a positive integer.

• A. Total number of divisors : $200$
  Number of even divisors : $140$
  Number of odd divisors : $30$
• B. Total number of divisors : $100$
  Number of even divisors : $160$
  Number of odd divisors : $20$
• C. Total number of divisors : $100$
  Number of even divisors : $140$
  Number of odd divisors : $40$
• D. Total number of divisors : $200$
  Number of even divisors : $180$
  Number of odd divisors : $20$

Answer 1

The correct option is D Total number of divisors : $200$

Number of even divisors : $180$
Number of odd divisors : $20$
$2.$ $\left(i\right)$ $n=1451520=2^9\times 3^4\times 5\times 7$
Total number of divisors $=(9+1)(4+1)(1+1)(1+1)$
$=10\times 5\times 2\times 2=200$

$\left(ii\right)$ Number of even divisors = Total number of divisors - number of odd divisors
$=200-(4+1)(1+1)(1+1)$
$=200-20=180$

$\left(iii\right)$ Number of divisors of the from $2m+1=$ all odd divisors i.e $5\times 2\times 2=20$