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How many odd factors does 180 have?

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garcmillan
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How many odd factors does 180 have? [#permalink] New post  19 Aug 2019, 02:20
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How many odd factors does 180 have?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 6
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ScottTargetTestPrep
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Re: How many odd factors does 180 have? [#permalink] New post  24 Aug 2019, 05:26
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garcmillan wrote:
How many odd factors does 180 have?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 6



First, we break 180 into its prime factors:

180 = 18 x 10 = 3^2 x 2^2 x 5

Recall the process of determining the total number of factors of a number: add 1 to the exponent of each of the prime factors and multiply those resulting numbers.

Similarly, to determine the number of odd factors of a number, we add 1 to the exponent of each of the odd prime factors and multiply those resulting numbers.

Since 3 has exponent 2 and 5 has exponent 1, we add 1 to 2 and 1 to 1 and we have 3 and 2. Multiplying 3 and 2, we have 6. So 180 has 6 odd factors.

Answer: E
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How many odd factors does 180 have? [#permalink] New post  19 Aug 2019, 03:33
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Number of odd factors of 180?
180 = 2^2•3^2•5
Number of factors =(2^0•2^1•2^2)•(3^0•3^1•3^2) •(5^0•5^1)
Number of odd factors = (3^0•3^1•3^2) •(5^0•5^1) = 3•2 = 6 factors

Answer E

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arockia
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Re: How many odd factors does 180 have? [#permalink] New post  22 Aug 2019, 07:49
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Prime factorize -->180=2^2*3^2*5
odd factors=3 and 5
no.of odd factors=Exponent of 3+1*Exponent of 5+1=(2+1)*(1+1)=6
option E)

Correct me if my solution is wrong :)
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Re: How many odd factors does 180 have? [#permalink] New post  22 Aug 2019, 08:17
garcmillan wrote:
How many odd factors does 180 have?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 6


180=2^2 3^2 5

Number of odd factors = (2+1) * (1+1) .............power of 3+1 and power of 5+1.........ignore 2 and its power to calculate odd factors.
=3*2 = 6 (option E)
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Re: How many odd factors does 180 have? [#permalink] New post  02 Dec 2023, 13:33
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Re: How many odd factors does 180 have? [#permalink]
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