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27 Nov 2013, 06:52
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Hi,
Can anyone please help me with the formula for finding the total no. of factors of an integer?
The usual way is prime factorization; then increasing the exponent of each prime factor by one; and multiplying the raised numbers.
E.g:
Q. Find the no. of factors of 90?
A.
90 = 2^1 x 3^2 x 5^1
So total factors = (1+1) x (2+1) x (1+1) = 2 x 3 x 2 = 12.
I have a test prep where solution actually doubles this answer saying that 12 are positive factors and there are as many negative factors.
So the total no. of factors should be 12 x 2 = 24.
But I researched a bit on the internet and almost everywhere they don't double the answer, i.e. they say answer is 12.
What is right on GMAT?
Thanks,
federite
Can anyone please help me with the formula for finding the total no. of factors of an integer?
The usual way is prime factorization; then increasing the exponent of each prime factor by one; and multiplying the raised numbers.
E.g:
Q. Find the no. of factors of 90?
A.
90 = 2^1 x 3^2 x 5^1
So total factors = (1+1) x (2+1) x (1+1) = 2 x 3 x 2 = 12.
I have a test prep where solution actually doubles this answer saying that 12 are positive factors and there are as many negative factors.
So the total no. of factors should be 12 x 2 = 24.
But I researched a bit on the internet and almost everywhere they don't double the answer, i.e. they say answer is 12.
What is right on GMAT?
Thanks,
federite
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THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
27 Nov 2013, 07:26
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federite
Factor is a "positive divisor" (at least on the GMAT). So, for example the factors of 4 are 1, 2, and 4 ONLY.
Finding the Number of Factors of an Integer
First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.
The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.
Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)
Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.
For more check: math-number-theory-88376.html
Questions to practice:
how-many-odd-positive-divisors-does-540-have-106082.html
how-many-factors-does-36-2-have-126422.html
how-many-different-positive-integers-are-factor-of-130628.html
how-many-distinct-positive-factors-does-30-030-have-144326.html
m02-72467.html
Hope this helps.
General Discussion
farful
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27 Nov 2013, 07:05
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You are correct - there are 12 factors in the number 90.
Generally, you do not include negative numbers. I'd be curious as to the actual wording of the question of the test prep.
Generally, you do not include negative numbers. I'd be curious as to the actual wording of the question of the test prep.
