courses › Pre-Algebra

Primes, prime factors, greatest common divisor, least common multiple.

Best in your head · no pen, no calculator why?

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Opens at level 14.

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Builds on: Division (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Spot the prime par 8 s not tried yet

  worked example

  Which number is prime?

  1. 93
  2. 133
  3. 71
  4. 129

  Answer: 71

  1. Test the primes up to √71: 2, 3, 5 and 7 (9² = 81 is past 71). None divides 71, so it is prime.
  2. The others: 93 = 3 × 31, 129 = 3 × 43, 133 = 7 × 19.

• Largest prime factor par 12 s not tried yet

  worked example

  What is the largest prime factor of 34?

  Answer: 17

  1. 34 = 2 × 17.
  2. The largest prime factor is 17.

• Greatest common divisor par 11 s not tried yet

  worked example

  What is the greatest common divisor of 198 and 154?

  Answer: 22

  1. 198 = 2 × 3² × 11 and 154 = 2 × 7 × 11.
  2. Take the primes they share, each at its lower power: 2 × 11 = 22.
  3. Check: 198 = 22 × 9 and 154 = 22 × 7, and 9 and 7 share no factor other than 1.

• Least common multiple par 11 s not tried yet

  worked example

  What is the least common multiple of 20 and 26?

  Answer: 260

  1. 20 = 2² × 5 and 26 = 2 × 13.
  2. Take every prime at its higher power: 2² × 5 × 13 = 260.
  3. Check: 20 × 26 ÷ 2 (their greatest common divisor) = 520 ÷ 2 = 260.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

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