Number Tree

This visualizes the relationship between prime numbers and composite numbers. Primes are the "seeds" of the number system - each birthing many numbers.

Hover on a prime to see all the numbers it "gives rise to" - its multiples. For example, hovering on 2 highlights all even numbers.

Hover on a composite to trace back to the primes it "comes from" - its prime factors. For example, 12 traces back to both 2 and 3.

Every composite number is uniquely determined by its prime factors (Fundamental Theorem of Arithmetic).

Primes are the basis for all numbers, but composites present their own fascinating side. As you interact with this tool, try hovering on the composites - how many lines do you generally see? 2? 3? 4?

You'll never see 5 lines tracing back to primes from any composite up to 500. But you will see 4. Which numbers are they? One way to find these composites with the most distinct prime factors is straightforward - multiply as many small primes as you can while keeping the product under 500. Try 210 - it's 2 × 3 × 5 × 7.