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Re: The number of distinct factors of 10 [#permalink]
Factorisation is the quickest way to solve it. Since after the factorisation of 10, we'll already have the prime factors of 10, we just need to factorize 21 to get the count for 210.
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Re: The number of distinct factors of 10 [#permalink]
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A doubt regarding this question

why we can't take -1 or -10 as a factor

as per the article -Technically, in the world of mathematics - the answer to this question is yes. There are negative factors and multiples of numbers. For example, -4 and -3 are factors of 12, -24 is a multiple of 3, and the factors of 4 would be -4, -2, -1, 1, 2, 4.

But what exactly does this mean in relation to the GRE and/or the GMAT?

For the GRE: This concept is mentioned in the ETS GRE Math Conventions PDF. You can find it here. The factors of an integer include both the positive and negative integers. This also applies for multiples.

Therefore, technically, if a GRE question were to ask "How many factors does 6 have?" The answer would be 8: (-6, -3, -2, -1, 1, 2, 3, 6). With that said, questions are very likely to specify "positive factors" or "positive integers" on the GRE. We haven't seen an official question before that required knowing that negative factors/multiples exist - but that doesn't mean those questions won't show up at all so you still want to be diligent about this. :)


we should consider them also.

P.S-why there is a restriction
never encountered this issue on GC
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Re: The number of distinct factors of 10 [#permalink]
2
Prime factors of 10- 1x10, 2x5
Prime factors of 210- 3x5x2x7

Hence Proved
4=4

therefore C

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Re: The number of distinct factors of 10 [#permalink]
sandy wrote:
Quantity A
Quantity B
The number of distinct factors of 10
The number of distinct prime factors of 210


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



I think distinct positive factor is the correct question
Total no Distinct factors of 10 are 8 then considering all the negative factors
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Re: The number of distinct factors of 10 [#permalink]
1
shubham2312 wrote:
A doubt regarding this question

why we can't take -1 or -10 as a factor

as per the article -Technically, in the world of mathematics - the answer to this question is yes. There are negative factors and multiples of numbers. For example, -4 and -3 are factors of 12, -24 is a multiple of 3, and the factors of 4 would be -4, -2, -1, 1, 2, 4.

But what exactly does this mean in relation to the GRE and/or the GMAT?

For the GRE: This concept is mentioned in the ETS GRE Math Conventions PDF. You can find it here. The factors of an integer include both the positive and negative integers. This also applies for multiples.

Therefore, technically, if a GRE question were to ask "How many factors does 6 have?" The answer would be 8: (-6, -3, -2, -1, 1, 2, 3, 6). With that said, questions are very likely to specify "positive factors" or "positive integers" on the GRE. We haven't seen an official question before that required knowing that negative factors/multiples exist - but that doesn't mean those questions won't show up at all so you still want to be diligent about this. :)


we should consider them also.

P.S-why there is a restriction
never encountered this issue on GC


So if we consider this should.t the answer to this question be A, since factors of 10 are 1,2,5,10,-1,-2,-5,-10 and prime factors for 210 are 2,5,7,3
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Re: The number of distinct factors of 10 [#permalink]
1
Quantity A

The number of distinct factors of 10

1, 2, 5, 10 = 4

or including negative factors

1, -1, 2, -2, 5, -5, 10, -10 = 8

Quantity B

The number of distinct prime factors of 210

2, 3, 5, 7 = 4

or including negative factors

2, -2, 3, -3, 5, -5, 7, -7 = 8

Either way, BOTH quantities are EQUAL

The answer is C.
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