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Divisor = Factor?

This topic has 1 expert reply and 2 member replies
JDesai01 Junior | Next Rank: 30 Posts Default Avatar
Joined
04 Jul 2008
Posted:
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Divisor = Factor?

Post Mon Jul 28, 2008 5:03 pm
Am I missing something when I conclude that a divisor is the same thing as a factor?

eg
What is the greatest common divisor of positive integers m and n?
(1) m is a prime number
(2) 2n = 7m

I probably wasted 30 seconds trying to figure out what they meant by divisor. Aren't they just asking for the greatest common factor?

BTW- answer is C (need both)

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Post Fri Aug 19, 2011 6:20 am
JDesai01 wrote:
What is the greatest common divisor of positive integers m and n?
(1) m is a prime number
(2) 2n = 7m

Thought I'd post a full solution to this question.

Statement 1:
If m is a prime number, it has exactly 2 divisors (1 and m), so this tells us that the GCD of m and n must be either 1 or m.
Since we know nothing about n, statement 1 is not sufficient.

Statement 2:
If 2n = 7m then we can rearrange the equation to get n = (7/2)m

Important aside: Notice that if m were to equal an odd number, then n would not be an integer. For example, if m=3, then n=21/2. Similarly, if m=11, then n=77/2. For n to be an integer, m must be even.

If m must be even, it could be the case that m=2 and n=7, in which case the GCD=1
Or it could be the case that m=4 and n=14, in which case the GCD=2
Or it could be the case that m=10 and n=35, in which case the GCD=5 . . . and so on.
Since we cannot determine the GCD with any certainty, statement 2 is not sufficient.

Statements 1 & 2 combined
From statement 1, we know that m is prime, and from statement 2, we know that m is even.
Since 2 is the only even prime number, we can conclude that m must equal 2.
If m=2, then n must equal 7, which means that the GCD must be 1.
Since we are able to determine the GCD with certainty, statements 1 & 2 combined are sufficient, and the answer is C

Cheers,
Brent

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artistocrat Master | Next Rank: 500 Posts Default Avatar
Joined
12 Mar 2008
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Post Mon Sep 01, 2008 6:50 am
The answer is C: If m is prime, the only way for 2n to be a factor of m is if m itself is 2, meaning n must be 7.

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sauryk Newbie | Next Rank: 10 Posts Default Avatar
Joined
17 Jul 2008
Posted:
2 messages
Post Mon Jul 28, 2008 8:00 pm
You are correct in assuming that divisor is the same as factor. Greatest Common Divisor (GCD) is same as greatest common factor (GCF) or highest common factor (HCF).

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