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26 Oct 2015, 18:53
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Hi I am confused on this and need detailed help with steps on how a particular step in this explanation is derived :
Question : Find the number of all the factors of 450
Answer was shown as 450 = \(\)2^1 x 3^2 x 5^2 and then this was further broken down to (1+1) x (2 + 1) x (2 + 1) = 18 factors
My confusion : where does the (1x1) x (2+1) x (2+1) come from?
I know the first part is the prime factorization right?
Question : Find the number of all the factors of 450
Answer was shown as 450 = \(\)2^1 x 3^2 x 5^2 and then this was further broken down to (1+1) x (2 + 1) x (2 + 1) = 18 factors
My confusion : where does the (1x1) x (2+1) x (2+1) come from?
I know the first part is the prime factorization right?
Archived Topic
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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27 Oct 2015, 12:21
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sagnik242
sagnik242 -
Yes, the first part is the prime factorization. The second part is a trick you can use to determine the number of unique factors. Following is a description:
Unique Factors Trick
There exists a “trick” for this type of problem that is worth knowing, but is not an essential priority to memorize. If such a question does come up, however, this rule will make solving it quite efficient. To find the number of unique factors of an integer:
1. Express the integer as a product of its prime factors, with each prime raised to its proper exponent. (In your example, it would be 2^1 x 3^2 x 5^2)
2. Strip the exponents off of the bases and “discard” the bases. In the example, you would now have 1, 2, and 2.
3. Add one to each exponent. In the example, now you would have 2, 3 and 3
4. Multiply those numbers, and that is the number of unique factors: 2 x 3 x 3 =18.
Hope this helps.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
