Video Explanation

Text Explanation

Step 1: Find the Prime Factorization
Break 2600 into easier pieces. Notice that 2600 can be written as 26 x 100. 

Now, factor each part:
•
• 

Putting it all together, the prime factorization of 2600 is

Step 2: List the Exponents
Look at the powers in the prime factorization:
• For 2, the exponent is 3.
• For 5, the exponent is 2.
• For 13, the exponent is 1.
So, the list of exponents is: 3, 2, and 1.

Step 3: Add 1 to Each Exponent
To account for the possibility of a prime factor not appearing in a divisor (that is, using an exponent of 0), add 1 to each exponent in your list:
• 3 becomes 4
• 2 becomes 3
• 1 becomes 2

Here are a couple of examples:

1 is a divisor of 2600

260 is a divisor of 2600

Each divisor of 2600 can have 0 to 3 2's, 0 to 2 5's and 0 to 1 13.

Step 4: Multiply the New Numbers Together
Now multiply these numbers:
4 × 3 = 12, and 12 × 2 = 24.

This final product, 24, represents the total number of divisors 2600 has. The related lesson below on Counting Factors of Large Numbers provides more detail on questions like these and why this approach works.