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S represents the set of positive integers that are factors of 7200. Ho [#permalink]
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08 Jul 2017, 11:41
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S represents the set of positive integers that are factors of 7200. How many integers in S are multiples of 72? A. 2 B. 5 C. 9 D. 10 E. 100
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Re: S represents the set of positive integers that are factors of 7200. Ho [#permalink]
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08 Jul 2017, 12:23
If 72x is a divisor of 7200, then 7200/72x is an integer, so, cancelling, 100/x is an integer. So x needs to be a divisor of 100. So that's the question  how many positive divisors does 100 have? If you know the method for counting divisors, you can get the answer quickly  prime factorize 100: 100 = 2^2 * 5^2 then look only at the exponents (2 and 2) : add 1 to each exponent, and multiply what you get. So 100 has (2 + 1)(2 + 1) = 3*3 = 9 divisors. Or you could list all nine of the divisors quite easily: 1, 2, 4, 5, 10, 20, 25, 50, 100
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Re: S represents the set of positive integers that are factors of 7200. Ho [#permalink]
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08 Jul 2017, 13:28
sonikavadhera wrote: S represents the set of positive integers that are factors of 7200. How many integers in S are multiples of 72?
A. 2 B. 5 C. 9 D. 10 E. 100 7200 = (2^5)*(3^2)*(5^2) 72 = (2^3)*(3^2) Multiple of 72 in set S can have 3 different powers of 2 (0,1,2) Multiple of 72 in set S can have 3 different powers of 5 (0,1,2) 72 can be multiplied with 3 different powers of 2 and still be a factor of 7200: (2^0), (2^1), (2^2) 72 can be multiplied with 3 different powers of 5 and still be a factor of 7200: (5^0), (5^1), (5^2) Therefore total combinations of multiples of 72, that are factors of 7200 is 3x3 = 9



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Re: S represents the set of positive integers that are factors of 7200. Ho [#permalink]
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31 Jul 2017, 06:34
hi bunuel, could you please post the solution .
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Re: S represents the set of positive integers that are factors of 7200. Ho [#permalink]
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31 Jul 2017, 06:38



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Re: S represents the set of positive integers that are factors of 7200. Ho [#permalink]
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01 Aug 2017, 01:23
IanStewart wrote: If 72x is a divisor of 7200, then 7200/72x is an integer, so, cancelling, 100/x is an integer. So x needs to be a divisor of 100. So that's the question  how many positive divisors does 100 have? If you know the method for counting divisors, you can get the answer quickly  prime factorize 100:
100 = 2^2 * 5^2
then look only at the exponents (2 and 2) : add 1 to each exponent, and multiply what you get. So 100 has (2 + 1)(2 + 1) = 3*3 = 9 divisors.
Or you could list all nine of the divisors quite easily: 1, 2, 4, 5, 10, 20, 25, 50, 100 shouldn't it be 10? why do we leave out 72 as a multiple ..



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Re: S represents the set of positive integers that are factors of 7200. Ho [#permalink]
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01 Aug 2017, 04:31
goforgmat wrote: IanStewart wrote: If 72x is a divisor of 7200, then 7200/72x is an integer, so, cancelling, 100/x is an integer. So x needs to be a divisor of 100. So that's the question  how many positive divisors does 100 have? If you know the method for counting divisors, you can get the answer quickly  prime factorize 100:
100 = 2^2 * 5^2
then look only at the exponents (2 and 2) : add 1 to each exponent, and multiply what you get. So 100 has (2 + 1)(2 + 1) = 3*3 = 9 divisors.
Or you could list all nine of the divisors quite easily: 1, 2, 4, 5, 10, 20, 25, 50, 100 shouldn't it be 10? why do we leave out 72 as a multiple .. Hi goforgmat, We are not leaving 72 as a multiple. Possible multiples are 72*1 = 72 72*2 = 144 72*4 = 288 72*5 = 360 72*10 = 720 72*20 = 1440 72*25 = 1800 72*50 = 3600 72*100 = 7200 The total is 9. Thanks.



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Re: S represents the set of positive integers that are factors of 7200. Ho [#permalink]
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02 Aug 2017, 12:29
sonikavadhera wrote: S represents the set of positive integers that are factors of 7200. How many integers in S are multiples of 72?
A. 2 B. 5 C. 9 D. 10 E. 100 7200 = 72 x 100. Thus, 72m is a factor of 7200 and also a multiple of 72, as long as m is a factor of 100. Since 100 = 2^2 x 5^2, 100 has (2 + 1) x (2 + 1) = 9 factors. Thus, there are 9 multiples of 72 that are also factors of 7200. Answer: C
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