Prime factorization explained for a 13-year-old — clear step-by-step guide with examples (age 13)

Learn prime factorization step-by-step for a 13-year-old. Clear definitions, methods (factor tree and division), worked examples, tips, and practice problems with answers.

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Prime factorization — step-by-step (for a 13-year-old)

What is prime factorization? It means writing a number as a product of prime numbers. A prime number is a number greater than 1 that has no divisors other than 1 and itself (examples: 2, 3, 5, 7, 11...).

Why this matters

Prime factorization helps with finding the greatest common factor (GCF), least common multiple (LCM), simplifying fractions, and solving many number problems.

Two easy methods

  1. Factor tree — keep breaking a number into two factors until all the pieces are prime.
  2. Repeated division — divide by the smallest prime you can, keep dividing the result, and record the primes you used.

Step-by-step algorithm (repeated division)

  1. Start with the smallest prime, 2. If the number is even, divide by 2. Write down 2.
  2. Keep dividing by 2 until it's no longer divisible by 2. Then try the next prime: 3, then 5, then 7, etc.
  3. Stop when the remaining number is 1 or is a prime itself (then include that prime).
  4. Write the result as primes multiplied, using exponents when a prime repeats (for example 2 × 2 × 3 = 22 × 3).

Worked examples

Example 1: 36

  • 36 is even, so divide by 2: 36 ÷ 2 = 18 (write down 2)
  • 18 is even, divide by 2: 18 ÷ 2 = 9 (write down another 2)
  • 9 is not divisible by 2. Try 3: 9 ÷ 3 = 3 (write down 3)
  • 3 is prime, so write down 3.

Primes: 2, 2, 3, 3. So 36 = 22 × 32.

Example 2: 84

  • 84 ÷ 2 = 42 (write 2)
  • 42 ÷ 2 = 21 (write 2)
  • 21 is not divisible by 2. Try 3: 21 ÷ 3 = 7 (write 3)
  • 7 is prime (write 7)

Primes: 2, 2, 3, 7. So 84 = 22 × 3 × 7.

Example 3: 360

  • 360 ÷ 2 = 180 (2)
  • 180 ÷ 2 = 90 (2)
  • 90 ÷ 2 = 45 (2)
  • 45 is not divisible by 2. Try 3: 45 ÷ 3 = 15 (3)
  • 15 ÷ 3 = 5 (3)
  • 5 is prime (5)

Primes: 2, 2, 2, 3, 3, 5. So 360 = 23 × 32 × 5.

How to check your answer

Multiply the prime factors (using exponents) to see if you get the original number. For example, for 36: 22 × 32 = 4 × 9 = 36.

Tips

  • Always try dividing by 2 first (it's the only even prime).
  • If a number is not divisible by 2, try 3, then 5, then 7, then 11, and so on.
  • Use a factor tree if you like pictures — it's the same idea but drawn out.
  • When a prime repeats, use exponents to write it neatly (for example 2 × 2 × 2 = 23).

Practice problems

  1. 56
  2. 100
  3. 231
  4. 98
  5. 225

Answers

  • 56 = 23 × 7 (because 56 = 2 × 28 = 2 × 2 × 14 = 2 × 2 × 2 × 7)
  • 100 = 22 × 52
  • 231 = 3 times; 7 times; 11 (231 = 3 × 77 = 3 × 7 × 11)
  • 98 = 2 times; 72
  • 225 = 32 × 52 (225 = 15 × 15 = (3 × 5) × (3 × 5))

If you want, I can show factor trees for any of these or give more practice problems at different difficulty levels.

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