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Real Number Detective

Prime Quest — Crack the Case of Every Number

Every number leaves a trail. Break them into prime factors, track down their HCF and LCM, sort the rational from the irrational and build the classic proof that √2, √3 and √5 can never be written as a fraction.

Detective Level 1 0 / 150 XP
Rookie Inspector
0Answered
0%Accuracy
0Best streak
0Blitz best

Choose Your Case

Achievements

How to Play

  1. Prime Factorization Lab — write a number as a product of primes. Type it as 2*2*3, 2 2 3 or 2^2 * 3 — order does not matter. Open the factor tree if you need a nudge.
  2. HCF & LCM Mission — answer with a number. Remember: HCF takes the smallest power of each common prime, LCM takes the largest power of every prime.
  3. Rational or Irrational Detective — pick the correct option. A fraction of integers (or a terminating or recurring decimal) is rational; a non-repeating decimal or a surd like √2 is irrational.
  4. Proof Arena — choose the next logical step, or arrange the shuffled proof steps into the right order.
  5. Decimal Expansion Race — reduce the fraction, then check the denominator. Only 2s and 5s give a terminating decimal.
  6. Number Blitz — answer as many mixed questions as you can before the timer ends. Build a streak for bonus points.

Press Esc to return home. Your progress is stored privately on this device only.