Factors · Primes & prime factorization · 3.2

Find the primes.

To find all primes up to 100, cross out the multiples of each prime (2, 3, 5, 7) — the “sieve”. What’s left are the primes. There are 25 primes under 100.

01 / THE IDEA

See it work.

The primes

Primes up to 100.

Highlighted numbers have exactly two factors.

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Watch the method

Find the primes

Cross out multiples of 2, 3, 5, 7 — primes remain.

1 / 1
2323
1

Prime or composite?

23 has only 1 and itself as factors.

prime\text{prime}
— / WHY IT WORKS

The idea underneath.

The sieve

Strike out every multiple of each prime; the survivors are prime. You only need primes up to √100 = 10.

Why it works

After removing multiples of 2, 3, 5, 7, the rest are prime.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Is 42 prime or composite?

1

Answer

Composite

EX 2medium

Is 17 prime or composite?

1

Answer

Prime

EX 3hard

Is 45 prime or composite?

1

Answer

Composite

04 / COMMON TRAPS

Where students slip.

Trap

Crossing out the prime itself.

Fix

Keep the prime; remove its larger multiples.

Trap

Forgetting to test 7.

Fix

Sieve with 2, 3, 5, AND 7 up to 100.

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 27 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
C2

Is 31 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
C3

Is 19 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
C4

Is 11 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
Apply

Apply (4)

A1

Is 3 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
A2

Is 17 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
A3

Is 44 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
A4

Is 43 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
Extension

Extension (4)

E1

Is 45 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
E2

Is 3 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
E3

Is 20 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.
E4

Is 48 prime or composite?

Need a hint?
  • Cross out multiples of 2, 3, 5, 7.
  • What remains is prime.