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The number of distinct prime factors of 20^6
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02 Feb 2026, 23:59
02 Feb 2026, 23:59
Expert Reply
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Question Stats:
95% (00:59) correct
4% (00:47) wrong based on 21 sessions
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Quantity A |
Quantity B |
The number of distinct prime factors of \(20^6\) |
The number of distinct prime factors of \(32^{10}\) |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
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Re: The number of distinct prime factors of 20^6
[#permalink]
15 Feb 2026, 16:41
15 Feb 2026, 16:41
1
A. The number of distinct prime factors of 20**6, needs to first be divided into prime factors. The factors of 20 are (4,5) (2,10) which are both equal to 2**2 * 5. Then we distribute the original exponent of 6, so we get 2**12 * 5**6 = 20**6. We have two distinct prime factors, {2,5}.
B. The number of distinct prime factors of 32**10, must also be divided into prime factors, if you know your powers of 2 then it is noticeably 2**5. However, if you don't just find the simple factors (2,16) (4,8) (8, 4) (16, 2) which all reduce to 2**5. Then we must distribute the original power of 10, making the equation = to 2**50. We have 1 distinct prime factor, {2}.
Therefore, option A is greater.
B. The number of distinct prime factors of 32**10, must also be divided into prime factors, if you know your powers of 2 then it is noticeably 2**5. However, if you don't just find the simple factors (2,16) (4,8) (8, 4) (16, 2) which all reduce to 2**5. Then we must distribute the original power of 10, making the equation = to 2**50. We have 1 distinct prime factor, {2}.
Therefore, option A is greater.
gmatclubot
Re: The number of distinct prime factors of 20^6 [#permalink]
15 Feb 2026, 16:41
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