The atoms of arithmetic
Every whole number above 1 either is prime, or splits into a product of primes in exactly one way. Once you can spot primes and factor at sight, simplifying fractions and finding common denominators becomes routine.
Prime numbers
A prime is a whole number greater than 1 with exactly two positive divisors: 1 and itself. The first few are 2, 3, 5, 7, 11, 13.
2 is the only even prime. 1 is not prime — it has only one divisor.
Composite numbers
A composite number has more than two positive divisors. 6 is composite (1, 2, 3, 6). Every composite breaks down into primes.
12 = 2 × 2 × 3 = 2² × 3.
Factors and multiples
A factor divides evenly into a number. A multiple is what you get by multiplying. Factors of 12: 1, 2, 3, 4, 6, 12. Multiples of 4: 4, 8, 12, 16…
GCF and LCM
The greatest common factor of two numbers is the largest factor they share. The least common multiple is the smallest multiple they share.
GCF(12, 18) = 6 · LCM(12, 18) = 36 · GCF × LCM = 12 × 18.
Divisibility shortcuts
Hands-on tools
Run the sieve, build a factor tree, or test any number against the divisibility rules.
Sieve of Eratosthenes
Click Step to cross off the next prime's multiples. Or hit Auto to sweep.
Click "Step" to begin. Numbers in orange are confirmed primes.
Factor tree
Type any whole number from 2 to 9999 — see it shatter into primes.
GCF and LCM via Venn diagram
Each circle shows one number's prime factors. The overlap is the GCF; the whole picture is the LCM.
Divisibility tester
Type a number — see which divisibility rules pass and why.
Quiz
Flashcards
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Daily challenge
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For teachers
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Reference
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Key facts
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