Prime Numbers Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy

Find the prime factorization of

180

Solution

1
Divide by 2: $180 \div 2 = 90$ . Divide again: $90 \div 2 = 45$ .
2
45 is odd, try 3: $45 \div 3 = 15$ . Again: $15 \div 3 = 5$ .
3
$5$ is prime, so stop. Prime factorization: $180 = 2^2 \times 3^2 \times 5$ .

Answer

2^2 \times 3^2 \times 5

To find the prime factorization, repeatedly divide by the smallest prime that divides evenly, working upward. Every composite number has a unique prime factorization (Fundamental Theorem of Arithmetic).

About Prime Numbers

Integers greater than 1 whose only positive divisors are 1 and themselves—they cannot be factored further.

Learn more about Prime Numbers →

More Prime Numbers Examples

Example 2 medium

Determine whether [formula] is prime.

Example 3 easy

List all prime numbers between 20 and 40.

Example 4 easy

Is [formula] prime or composite?

← All Prime Numbers Examples Prime Numbers Concept

Related Concepts

Factors Divisibility Intuition Composite Numbers Prime Factorization