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Bunuel
What is the total number of positive factors of 6400?

A. 24
B. 27
C. 54
D. 68
E. 72

What is the total number of different divisors including 1 and the number that can divide the number 6400?
(1) 24 (2) 27 (3) 54 (4) 68

CONCEPT: If \(N = a^p*b^q*c^r...\)
where a, b, c... are distinct primes
Number of factors of \(N = (p+1)*(q+1)*(r+1)*...\)

\(6400 = 64*100 = 2*8*5^2\)

Factors of 6400 = (8+1)*(2+1) = 27

Answer: Option B
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Bunuel
What is the total number of positive factors of 6400?

A. 24
B. 27
C. 54
D. 68
E. 72

What is the total number of different divisors including 1 and the number that can divide the number 6400?
(1) 24 (2) 27 (3) 54 (4) 68

Asked: What is the total number of positive factors of 6400?

\(6400 = 2^8*5^2\)
The total number of positive factors of 6400 = 9*3 = 27

IMO B
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6400 is a perfect square (80*80), so just looking at the answers, the only odd number is 27.
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Bunuel
What is the total number of positive factors of 6400?

A. 24
B. 27
C. 54
D. 68
E. 72

What is the total number of different divisors including 1 and the number that can divide the number 6400?
(1) 24 (2) 27 (3) 54 (4) 68

Solution:

Getting 6400 into prime factors, we have:

6400 = 64 x 100 = 2^8 x 5^2

Thus, 6400 has (8+1)(2+1) = 9 x 3 = 27.

Answer: B
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