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16,000 has how many positive divisors?
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09 Jan 2026, 10:11
09 Jan 2026, 10:11
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16,000 has how many positive divisors?
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Re: 16,000 has how many positive divisors?
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31 Jan 2026, 12:49
31 Jan 2026, 12:49
Expert Reply
16,000 has 32 positive divisors.
Prime factorize:
$$
\(16,000=16 \times 1,000=2^4 \times\left(10^3\right)=2^4 \times(2 \times 5)^3=2^7 \times 5^3 \)
$$
If $\(n=p_1^a p_2^b\)$, then the number of positive divisors is $\((a+1)(b+1)\)$.
Here that is $\((7+1)(3+1)=8 \times 4=32\)$.
Prime factorize:
$$
\(16,000=16 \times 1,000=2^4 \times\left(10^3\right)=2^4 \times(2 \times 5)^3=2^7 \times 5^3 \)
$$
If $\(n=p_1^a p_2^b\)$, then the number of positive divisors is $\((a+1)(b+1)\)$.
Here that is $\((7+1)(3+1)=8 \times 4=32\)$.
gmatclubot
Re: 16,000 has how many positive divisors? [#permalink]
31 Jan 2026, 12:49
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