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What is the number of positive integers less than 500 which have an odd number of divisors?
A. 18
B. 20
C. 22
D. 24
E. 26
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A. 18
B. 20
C. 22
D. 24
E. 26
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Bunuel
Solution:
- Theory: If an integer has odd number of factors/divisor, the integer has to be prefect square
- For example: \(16 = 2^4\) has \(4+1=5\) factors
- So, integers less than 500 having odd factors will be
- \(1^2=1\)
- \(2^2=4\)
- \(3^2=9\)
- \(..\)
- \(..\)
- \(21^2=441\)
- \(22^2=484\)
- So, 22 such integers
Hence the right answer is Option C
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General Discussion
Odd number of divisors(factors).
All perfect squares have odd no. of factors.
so 22 number of positive integers less than 500 which have an odd number of divisors
All perfect squares have odd no. of factors.
so 22 number of positive integers less than 500 which have an odd number of divisors
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