Question:
How many positive factors (divisors) does 360 have?
How many positive factors (divisors) does 360 have?
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Prime factorise, then multiply (exponent + 1) for each prime.
Updated On: Jul 8, 2026
- 24
- 20
- 18
- 12
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The Correct Option is A
Solution and Explanation
Step 1: Prime factorise 360.
\[360 = 2^3 \times 3^2 \times 5^1\] Step 2: Apply the number-of-divisors formula.
If \(N = p^a q^b r^c\), the count of divisors is \((a+1)(b+1)(c+1)\).
Step 3: Substitute.
\[(3+1)(2+1)(1+1) = 4 \times 3 \times 2 = \boxed{24}\]
\[360 = 2^3 \times 3^2 \times 5^1\] Step 2: Apply the number-of-divisors formula.
If \(N = p^a q^b r^c\), the count of divisors is \((a+1)(b+1)(c+1)\).
Step 3: Substitute.
\[(3+1)(2+1)(1+1) = 4 \times 3 \times 2 = \boxed{24}\]
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