Question:
The number of positive divisors of 67375 which are greater than 5 is
The number of positive divisors of 67375 which are greater than 5 is
Updated On: May 12, 2024
- 24
- 23
- 22
- 5
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The Correct Option is B
Solution and Explanation
$67375$ can be written as $67375 = 5^3 \times 11 \times 7^2$
$= 125 \times 11 \times 49$
$(125, 11) = 1, (49, 11) = 1, (125, 49) = 1$
$\therefore$ Number of divisor of $67375$ = number of divisor of $(125) \times$ number of divisor of $(11) \times$ number of divisor of (49)
$= 4 \times 2 \times 3 = 24$
Number of divisor which are greater than 5 is = 24 - 1 = 23
$= 125 \times 11 \times 49$
$(125, 11) = 1, (49, 11) = 1, (125, 49) = 1$
$\therefore$ Number of divisor of $67375$ = number of divisor of $(125) \times$ number of divisor of $(11) \times$ number of divisor of (49)
$= 4 \times 2 \times 3 = 24$
Number of divisor which are greater than 5 is = 24 - 1 = 23
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Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects