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Intern  B
Joined: 27 Jul 2011
Posts: 49
If A is a factor of BC , and GCD(A,B)=1 , then A is a factor  [#permalink]

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If A is a factor of BC , and GCD(A,B)=1 , then A is a factor of C.

If A is a factor of B and B is a factor of A, A = B then or A=-B.

These statements are found on GMATclub Math workbook. Could someone please explain the statements as I have trouble understanding them, could someone also please give examples to both statements. Thanks in advance.
Intern  Joined: 23 Jan 2014
Posts: 14
GMAT 1: 780 Q51 V45 GPA: 4
Re: If A is a factor of BC , and GCD(A,B)=1 , then A is a factor  [#permalink]

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The first statement means: if A is a factor of BC and A and B have no common factors than A divide C.
For example A=2 B=3 and C=4. A is a factor (=divide) BC which is 12. But A and B have no common factor. Therefore A divide C (2 divides 4).

The second statements is more straightforward. It just means that if a number divides another one for example 2 divides 4, then the only way it can be divided by this number as well is that it is the same number or the opposite.

Hope this clarify things
Math Expert V
Joined: 02 Sep 2009
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Re: If A is a factor of BC , and GCD(A,B)=1 , then A is a factor  [#permalink]

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smartyman wrote:
If A is a factor of BC , and GCD(A,B)=1 , then A is a factor of C.

If A is a factor of B and B is a factor of A, A = B then or A=-B.

These statements are found on GMATclub Math workbook. Could someone please explain the statements as I have trouble understanding them, could someone also please give examples to both statements. Thanks in advance.

If a is a factor of bc, and gcd(a,b)=1, then a is a factor of c.

Say $$a=2$$, $$b=3$$ ($$gcd(a,b)=gcd(2,3)=1$$), and $$c=4$$.

$$a=2$$ IS a factor of $$bc=12$$, and $$a=2$$ IS a factor of $$c$$.

OR: if $$a$$ is a factor of $$bc$$ and NOT a factor of $$b$$, then it must be a factor of $$c$$.

Hope it's clear.
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Re: If A is a factor of BC , and GCD(A,B)=1 , then A is a factor  [#permalink]

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_________________ Re: If A is a factor of BC , and GCD(A,B)=1 , then A is a factor   [#permalink] 25 Feb 2019, 09:21
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