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# Why????? If N is a positive integer, is the units digits of

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Why????? If N is a positive integer, is the units digits of [#permalink]  27 Jul 2006, 14:55
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Why?????

If N is a positive integer, is the units digits of N iqual to 0 (zero)

1) 14 and 35 are factors of N
2) N=(2^5)*(3^2)*(5^7)*(7^6)

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Joined: 07 Jul 2005
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Re: DS - Units Digit [#permalink]  27 Jul 2006, 14:59
MANRED wrote:
Why?????

If N is a positive integer, is the units digits of N iqual to 0 (zero)

1) 14 and 35 are factors of N
2) N=(2^5)*(3^2)*(5^7)*(7^6)

Yes, D it is.
I. since 14 and 35 are factors, its LCM is : 2*7*5 = 70 ..Now, the min. value N can be have is 70 or 70*x (x being +ve integer) .. Implies units digit is 0.

II. N's value is given, so we can calculate if units digit is 0 or not.

D.
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Re: DS - Units Digit [#permalink]  27 Jul 2006, 16:54
MANRED wrote:
Why?????

If N is a positive integer, is the units digits of N iqual to 0 (zero)

1) 14 and 35 are factors of N
2) N=(2^5)*(3^2)*(5^7)*(7^6)

Yes or No question...

1. If 14 and 35 are factors of N, we know that 14 = 2*7 and 35 = 5*7. If you multiply 2*5*7 = unit digit is equal to 0. Yes...Suff...

2. Since we are only interested in the units digit only,
2^5 = some number with unit digit of 2
3^2= 9
5^7= some number with unit digit of 5
7^6= some number with unit digit of 9
so 2*9*9*5 = leads to unit digit of 0... Yes... Suff..

D
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D

1) 14 and 35 are factors.

LCM of 14 and 35 = 70
hence the mininum number can be 70 and other number can be 70 * x

2)
Unit digit of 2^5 = 2
Unit digit of 3^2 = 9
Unit digit of 5^x = 5
Unit digit of 7^6 = 3

Unit digit of N = Unit digit of (2*9*5*3) = 0
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