Question

Which of these numbers has the most number of divisors?

• A. 200
• B. 156
• C. 240
• D. 172

Answer 1

Answer:

C. 240

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).