Express 252 as a product of prime factors.

Given data

• Number to factorize into primes: 252.

Concept / Approach

• Use successive division by the smallest possible prime at each step (prime factor tree).
• Stop when all factors are prime; then group equal primes into powers.

Step-by-step calculation

252 ÷ 2 = 126126 ÷ 2 = 6363 ÷ 3 = 2121 ÷ 3 = 77 is prime ⇒ stop.Thus 252 = 2 × 2 × 3 × 3 × 7 = 2^2 × 3^2 × 7.

Verification / Alternative

Multiply back: 2^2 × 3^2 × 7 = 4 × 9 × 7 = 36 × 7 = 252 ✔

Common pitfalls

• Missing one of the 3's (since 63 = 3 × 21 = 3 × 3 × 7).
• Stopping at a composite factor (e.g., 21) instead of fully factoring to primes.

Final Answer

Prime factorization: 2^2 × 3^2 × 7.