Factors · Primes & prime factorization · 3.1

Prime vs composite.

A prime number has exactly two factors: 1 and itself (like 2, 3, 5, 7, 11). A composite number has more than two factors (like 12). The number 1 is neither.

01 / THE IDEA

See it work.

Watch the method

Prime vs composite

13 is prime; 12 is composite.

1 / 1
1313
1

Prime or composite?

13 has only 1 and itself as factors.

prime\text{prime}
— / WHY IT WORKS

The idea underneath.

Count the factors

Exactly two factors → prime; more than two → composite. 1 has only one factor, so it’s neither.

Why it works

7 only divides by 1 and 7.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Is 38 prime or composite?

1

Answer

Composite

EX 2medium

Is 25 prime or composite?

1

Answer

Composite

EX 3hard

Is 15 prime or composite?

1

Answer

Composite

04 / COMMON TRAPS

Where students slip.

Trap

Calling 1 prime.

Fix

1 has a single factor, so it’s neither prime nor composite.

Trap

Thinking all odd numbers are prime.

Fix

9 and 15 are odd but composite.

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

Is 33 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
C2

Is 16 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
C3

Is 27 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
C4

Is 5 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
Apply

Apply (4)

A1

Is 46 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
A2

Is 13 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
A3

Is 22 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
A4

Is 26 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
Extension

Extension (4)

E1

Is 11 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
E2

Is 33 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
E3

Is 40 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.
E4

Is 50 prime or composite?

Need a hint?
  • Count the factors.
  • Exactly two → prime.