Factors & Multiples Playground

Pick a number and discover all its factor pairs as colorful rectangles. Learn what makes a number prime or composite, then challenge yourself with GCF and LCM puzzles.

Pick a Number
12
2 to 50
Composite Number3 factor pairs

Factor Pairs as Rectangles

1 × 12
(1, 12)
2 × 6
(2, 6)
3 × 4
(3, 4)

All Factors of 12

1234612

First 8 Multiples of 12

1224364860728496...

Factors & Multiples Reference

What Are Factors?

A factor is a number that divides evenly into another number.

Every number has at least two factors: 1 and itself.

  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Factors of 7: 1, 7 (prime!)
  • Factor pairs of 12: (1,12), (2,6), (3,4)

Prime vs Composite

A prime number has exactly 2 factors: 1 and itself.

A composite number has more than 2 factors.

  • Prime: 2, 3, 5, 7, 11, 13, 17, 19...
  • Composite: 4, 6, 8, 9, 10, 12...
  • Special: 1 is neither prime nor composite

GCF and LCM

The GCF (Greatest Common Factor) is the largest factor shared by two numbers.

The LCM (Least Common Multiple) is the smallest multiple shared by two numbers.

  • GCF(12, 8) = 4
  • LCM(4, 6) = 12

Multiples

A multiple is what you get when you multiply a number by 1, 2, 3, 4, ...

  • Multiples of 3: 3, 6, 9, 12, 15...
  • Multiples of 5: 5, 10, 15, 20, 25...
  • Every number is a multiple of its factors