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Math Language - 'Factor'

Problem Solving — algebra and arithmetic
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by mindful » Tue Jul 07, 2015 6:38 am
Hello,

Very new to the prep. Sorry if this is a stupid question. It would be nice to receive your reply to each of these parts.

1. What do folks understand when they see or hear the phrase "n factors of b"?

2. Do you automatically understand this to mean b multiplied by itself n times?

3. The way I understood this is as n different factors of b. Example 3 factors of 2500? I don't immediately see it as 2500*2500*2500. I would say 3 factors of 2500 are 5, 25, and 100. How do I clarify or distinguish between the two possible meanings of this phrase. Is the meaning in the second statement the standard accepted meaning of this phrase?


Thanks!
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by Ian Stewart » Tue Jul 07, 2015 7:51 am
The phrase "two factors of 10" means "two divisors of 10", so would refer to two numbers in the list: 1, 2, 5, 10.

But that phrase is, in some sources, used imprecisely to mean something more like "two factors equal to 10", when the term "factor" is being used to describe a term in a product. So some sources will say things like "100 is equal to the product of two factors of 10", which is a laborious and unclear way of saying "100 equals 10 times 10". If you're studying from a source that uses the phrase in this more colloquial way, you may have to judge by context what is intended. You won't encounter that usage in an actual GMAT question though.
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by mindful » Tue Jul 07, 2015 8:01 am
Thank you for the clarification! I wasn't sure if it was some usage that I wasn't aware of.
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by [email protected] » Tue Jul 07, 2015 9:02 am
Hi mindful,

Have you come across any specific GMAT prompts that use this language and are giving you trouble? It would help to have 'context' for what you're describing. As such, you can/should post any questions that are giving you trouble (or that you're unclear about), and the other users and Experts should be able to help you to work through whatever points are unclear.

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by mindful » Tue Jul 07, 2015 9:59 am
Actually it was a wonderful video on a test prep site I was watching that used 'm factors of b' to describe b to the power m. I understand what b to the power m means...I understood the video also. but I guess I was just surprised by the phrase which my brain processed differently. I have a tendency to get pedantic or nitpicky with words...something I should be careful about. This seems common usage (Not sure if used on the GMAT). I asked my family for instance; they understood the phrase without any problems.

Example: https://www.csun.edu/~ayk38384/notes/mod2/ch1.htm On this page you will find the following sentence:
" In general, b^m*b^n means m factors of b times n factors of b. There are then m + n factors of b, which may be written as bm+n. When multiplying two or more expressions with the same base, simply write the base and add the exponents."

(It could simply be I am so far away from the math that I have forgotten that in such cases bases are called factors too.) But, no, haven't come across a GMAT ques with this phrase...
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