Factors · Primes & prime factorization · 3.3

Prime factorization.

Every composite number breaks down into a product of primes. A factor tree splits the number into factors over and over until every leaf is prime. 36 = 2×2×3×3.

01 / THE IDEA

See it work.

Factor tree

Split until every leaf is prime.

The prime leaves are the prime factorization.

362182933

36 = 2² × 3²

Watch the method

Prime factorization

36 → 6×6 → (2×3)(2×3) = 2×2×3×3.

1 / 2
3636
1

Build a factor tree

Split into factors until every leaf is prime.

2×2×3×32 \times 2 \times 3 \times 3
2

Write the prime factorization

Collect the primes (use exponents for repeats).

36=22×3236 = 2^{2} \times 3^{2}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type primes, e.g. 2^3·3.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Down to primes

Keep splitting composite factors; the prime leaves multiplied together rebuild the number.

Why it works

36 = 2·2·3·3.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write the prime factorization of 16.

1

Build a factor tree

Split into factors until every leaf is prime. 2 × 2 × 2 × 2

2

Write the prime factorization

Collect the primes (use exponents for repeats). 16 = 2^4

EX 2medium

Write the prime factorization of 28.

1

Build a factor tree

Split into factors until every leaf is prime. 2 × 2 × 7

2

Write the prime factorization

Collect the primes (use exponents for repeats). 28 = 2^2 × 7

EX 3hard

Write the prime factorization of 48.

1

Build a factor tree

Split into factors until every leaf is prime. 2 × 2 × 2 × 2 × 3

2

Write the prime factorization

Collect the primes (use exponents for repeats). 48 = 2^4 × 3

04 / COMMON TRAPS

Where students slip.

Trap

Stopping before the leaves are prime.

Fix

Keep splitting until every leaf is prime.

Trap

Leaving out a repeated prime.

Fix

Include every prime leaf, repeats and all.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Write the prime factorization of 30.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
C2

Write the prime factorization of 18.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
C3

Write the prime factorization of 60.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
C4

Write the prime factorization of 90.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
Apply

Apply (4)

A1

Write the prime factorization of 45.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
A2

Write the prime factorization of 30.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
A3

Write the prime factorization of 50.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
A4

Write the prime factorization of 30.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
Extension

Extension (4)

E1

Write the prime factorization of 72.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
E2

Write the prime factorization of 24.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
E3

Write the prime factorization of 28.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.
E4

Write the prime factorization of 80.

Need a hint?
  • Split the number into a factor pair.
  • Keep splitting until all leaves are prime.