How many factors does 400 have?
2025
How many factors does 400 have?
- A.
8
- B.
10
- C.
12
- D.
15
Attempted by 188 students.
Show answer & explanation
Correct answer: D
Prime factorization: 400 = 2^4 × 5^2.
Rule: If a number's prime factorization has exponents a, b, ... then the number of positive factors is (a + 1)(b + 1) ... .
Apply: The exponents are 4 and 2, so (4 + 1) × (2 + 1) = 5 × 3 = 15.
Therefore the number of positive factors of 400 is 15.