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How many odd factors does the number 2100 have ?
[#permalink]
02 Nov 2020, 04:15
02 Nov 2020, 04:15
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Difficulty:
25%
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Question Stats:
67% (00:48) correct
33%
(01:27)
wrong
based on 55
sessions
How many odd factors does the number 2100 have ?
A. 2
B. 3
C. 6
D. 9
E. 12
A. 2
B. 3
C. 6
D. 9
E. 12
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Joined: 16 Feb 2015
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Location: United States
Re: How many odd factors does the number 2100 have ?
[#permalink]
02 Nov 2020, 04:24
02 Nov 2020, 04:24
Explanation:
2100 = 3x7x10x10
2100 = 3x7x2x5x2x5
2100 = 2^2x3^1x5^2x7^1
except 2 all will give odd factors
So, Number of odd factors are = (2+1)(1+1)(1+1) = 3x2x2 = 12
IMO-E
2100 = 3x7x10x10
2100 = 3x7x2x5x2x5
2100 = 2^2x3^1x5^2x7^1
except 2 all will give odd factors
So, Number of odd factors are = (2+1)(1+1)(1+1) = 3x2x2 = 12
IMO-E
Re: How many odd factors does the number 2100 have ?
[#permalink]
02 Nov 2020, 04:33
02 Nov 2020, 04:33
How many odd factors does the number 2100 have ?
To solve this, do prime factorization:
2100=7*3*(5^2)*(2^2)
Odd not have 2 as a prime factor
so consider exponents of 7, 3 and 5:
Odd factors=(1+1)(1+1)(2+1)=2*2*3=12
CORRECT ANSWER: E
To solve this, do prime factorization:
2100=7*3*(5^2)*(2^2)
Odd not have 2 as a prime factor
so consider exponents of 7, 3 and 5:
Odd factors=(1+1)(1+1)(2+1)=2*2*3=12
CORRECT ANSWER: E
