What is the prime factorization of 2025?

To find the prime factorization of 2025, we follow these steps:

Divide by 5: Since 2025 ends in 5, it is divisible by 5. 2025 ÷ 5 = 405

Divide 405 by 5: 405 also ends in 5, so it is divisible by 5. 405 ÷ 5 = 81

Divide 81 by 3: 81 is divisible by 3 because the sum of its digits (8 + 1 = 9) is divisible by 3. 81 ÷ 3 = 27

Divide 27 by 3: 27 is divisible by 3 because the sum of its digits (2 + 7 = 9) is divisible by 3. 27 ÷ 3 = 9

Divide 9 by 3: 9 is divisible by 3 because the sum of its digits (9) is divisible by 3. 9 ÷ 3 = 3

Divide 3 by 3: 3 is divisible by 3. 3 ÷ 3 = 1

Now, we have broken 2025 down completely into prime factors. The prime factorization is:

2025 = 5 × 5 × 3 × 3 × 3 × 3

Or written with exponents:

2025 = 5² × 3⁴

This is the prime factorization of 2025.