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

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

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28 Jan 2014, 17:59
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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.
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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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29 Jan 2014, 08:49
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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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29 Jan 2014, 04:36
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
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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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25 Feb 2019, 09:21
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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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