Which of these numbers has the most number of divisors?
A200
B156
C240
D172
Answer:
C. 240
Read Explanation:
1. Prime Factorization:
Find the prime factors of each number:
A) 200 = 2^3 * 5^2
B) 240 = 2^4 3 5
C) 156 = 2^2 3 13
D) 172 = 2^2 * 43
2. Calculate the Number of Divisors:
To find the total number of divisors, follow these steps:
Add 1 to each of the exponents in the prime factorization.
Multiply the resulting numbers together.
A) 200: (3+1) (2+1) = 4 3 = 12 divisors
B) 240: (4+1) (1+1) (1+1) = 5 2 2 = 20 divisors
C) 156: (2+1) (1+1) (1+1) = 3 2 2 = 12 divisors
D) 172: (2+1) (1+1) = 3 2 = 6 divisors
Answer:
240 has the most number of divisors (20 divisors).