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# If z is an integer, is z prime?

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Re: If z is an integer, is z prime? [#permalink]
What if z is a negative integer that fulfils those conditions? Like -7.
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Re: If z is an integer, is z prime? [#permalink]
supershroomy wrote:
What if z is a negative integer that fulfils those conditions? Like -7.

as far as i know, GCD can be +ve only, starting from 1.
and when we are calculating distinct factors we first prime factorize the number to find a total number of distinct factors. which means dist. factors are always positive since prime numbers can never be -ve.

Bunuel chetan2u please correct me if i'm wrong
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If z is an integer, is z prime? [#permalink]
energetics wrote:
If z is an integer, is z prime?

(1) The greatest common divisor of z and 140 is 7.

(2) The sum of the distinct factors of z is less than 10.

Yes apurv09, you are correct. In GMAT, we talk of only positive factors.

(1) The greatest common divisor of z and 140 is 7.
$$140=2^2*5*7$$
So z will be 7x, where x can be any value except multiples of 2 or 5.
So x=1, then z=7......z is prime.
If x=3, then z=3*7=21...z is not prime.
Insufficient

(2) The sum of the distinct factors of z is less than 10.
This means that z<10 for sure.
It can be 1, 2, 3, 4, 5, or 7.
If 1 and 4, then z is not prime.
If 2, 3, 5 or 7, then z is prime.
It cannot be 6, because the sum of factors is 1+2+3+6=12.
It cannot be 8, because the sum of factors is 1+2+4+8=15.
Insufficient

Combined
Only 7 is common in two statements
Sufficient as z is prime.

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Re: If z is an integer, is z prime? [#permalink]
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Re: If z is an integer, is z prime? [#permalink]
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