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# How many 3 digit numbers have exactly 3 factors

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Director
Joined: 19 Oct 2018
Posts: 772
Location: India
How many 3 digit numbers have exactly 3 factors  [#permalink]

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25 Apr 2019, 04:12
3
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:18) correct 37% (01:40) wrong based on 43 sessions

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How many 3 digit numbers have exactly 3 factors?

A. 15
B. 22
C. 21
D. 23
E. 7
Intern
Joined: 24 Apr 2019
Posts: 19
Re: How many 3 digit numbers have exactly 3 factors  [#permalink]

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25 Apr 2019, 04:17
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nick1816 wrote:
How many 3 digit numbers have exactly 3 factors?

A. 15
B. 22
C. 21
D. 23
E. 7

Only way a number has exactly 3 factors is when it is a square of a prime number.

So, Starting from 100(square of 10) to 961(Square of 31)

We have to find number of prime numbers between 10 and 31.

Thats is 11,13,17,19,23,29,31.

There are 7 such numbers. So, IMO, Option E.
Manager
Joined: 18 Dec 2017
Posts: 162
Re: How many 3 digit numbers have exactly 3 factors  [#permalink]

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02 Aug 2019, 09:47
2
nick1816 wrote:
How many 3 digit numbers have exactly 3 factors?

A. 15
B. 22
C. 21
D. 23
E. 7

My Approach.
You should realize only a perfect square has odd number of factors.
16 has 1,2,4,8,16. 25 has 1,5,25.
Think of the least 3 digit perfect square. 121. Hmm 1,11,121. Works.
12 won't work but 13 will. 14 won't work but 17 does. So a pattern should click now.
11,13,17,19,23,29. I actually stopped here and thought 6. but there is no option of 6 (Thank God)
so thought wait 31 works too.

Hence E.
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Re: How many 3 digit numbers have exactly 3 factors   [#permalink] 02 Aug 2019, 09:47
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