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How many 2-digit numbers have exactly 3 factors?
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01 Jul 2021, 07:59
01 Jul 2021, 07:59
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How many 2-digit numbers have exactly 3 factors?
A. 6
B. 4
C. 1
D. 2
E. None of the above
A. 6
B. 4
C. 1
D. 2
E. None of the above
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Joined: 10 Apr 2015
Posts: 6218
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Re: How many 2-digit numbers have exactly 3 factors?
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01 Jul 2021, 08:04
01 Jul 2021, 08:04
1
Carcass wrote:
How many 2-digit numbers have exactly 3 factors?
A. 6
B. 4
C. 1
D. 2
E. None of the above
A. 6
B. 4
C. 1
D. 2
E. None of the above
IMPORTANT CONCEPT #1: A perfect square (the square of an integer) will always have an ODD number of positive divisors.
For example, 25 has 3 positive divisors: 1, 5 and 25
Likewise, 16 has 5 positive divisors 1, 2, 4, 8 and 16
And 100 has 9 positive divisors 1, 2, 4, 5, 10, 20, 25, 50 and 100)
IMPORTANT CONCEPT #2: The square of a PRIME number will have exactly 3 positive divisors.
For example, 9 has 3 positive divisors: 1, 3 and 9
Likewise, 49 has 3 positive divisors 1, 7, and 49
So, the 2-digit numbers with exactly 3 factors are 25 (aka 5²) and 49 (aka 7²)
Answer: D
Cheers,
Brent
Re: How many 2-digit numbers have exactly 3 factors?
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22 Jul 2023, 20:12
22 Jul 2023, 20:12
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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