How many factors of 330 are odd numbers greater than 1?
A. 3
B. 4
C. 5
D. 6
E. 7
*An answer will be posted in 2 days.
How many factors of 330 are odd numbers greater than 1?
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- Max@Math Revolution
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IMO E
330 = 2*3*5*11
for factors to be odd we don't need multiple of 2
therefore number of odd factors = 1*2*2*2 = 8
8 is total number of odd factors but it also has 1 as a factor so subtract 1 from 8
8-1=7
Hence total number of odd factors except 1 = 7
330 = 2*3*5*11
for factors to be odd we don't need multiple of 2
therefore number of odd factors = 1*2*2*2 = 8
8 is total number of odd factors but it also has 1 as a factor so subtract 1 from 8
8-1=7
Hence total number of odd factors except 1 = 7
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330 is a pretty small #, so it wouldn't take long to LIST all of the odd factors.Max@Math Revolution wrote:How many factors of 330 are odd numbers greater than 1?
A. 3
B. 4
C. 5
D. 6
E. 7
*An answer will be posted in 2 days.
We'll use the fact that 330 = (2)(3)(5)(11) AND the fact that ODD x ODD = ODD
So, the ODD factors of 330 are:
- 3
- 5
- 11
- (3)(5) [we need not evaluate this since we'll just going to count the factors in our list]
- (3)(11)
- (5)(11)
- (3)(5)(11)
Done!
Answer: E
- Max@Math Revolution
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If we calculate, we get 330=2*3*5*11. We are trying to find odd factors. So we have to find 3*5*11. From (1+1)(1+1)(1+1)=8, we only have to get rid of 1. The answer is 7. Hence, the correct answer is E.
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