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Divisors of a number

CombinatoricsEasy

How many positive integers divide $360$ exactly?

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Hint

Factor the number into primes and think about the allowed exponents.

Solution

Factor $360 = 2^{3} \times 3^{2} \times 5$ .
A divisor takes the exponent of $2$ from $0$ to $3$ , of $3$ from $0$ to $2$ , and of $5$ from $0$ to $1$ , all independently.
The count is $4 \times 3 \times 2 = 24$ .

Answer: $24$