Understanding Factors and Prime Factorization

🔹 What Are Factors?

A factor of a number is a whole number that divides exactly into another number, leaving no remainder. In other words, if you can multiply two whole numbers to get another number, then both of those numbers are factors of the product.

Example: The factors of 24 are:

1 × 24
2 × 12
3 × 8
4 × 6

So, the factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.

Find all factors of a number with our Factor Checker tool.

🟢 Factor Pairs

A factor pair is a set of two whole numbers that multiply together to give the original number.

Example (24):

1 × 24
2 × 12
3 × 8
4 × 6

Factor pairs of 24: (1, 24), (2, 12), (3, 8), (4, 6)

🔴 Prime Factorization

Prime factorization is the process of expressing a number as a product of its prime numbers. A prime number is greater than 1 and only divisible by 1 and itself.

To find the prime factorization of 24:

24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1

So, the prime factorization of 24 is: 2 × 2 × 2 × 3 = 2³ × 3

This breakdown can also be visualized with a factor tree.

Find the prime factorization of a number with our Prime Factorization Calculator tool.

🟨 Explore Factor Pages

Click on any number below to view its full factor list, factor pairs, and prime factorization.

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