What Are the Factors of 4?
Lay out 4 coins and you can make one row of 4, or two rows of 2. That is what factors look like. A factor is a whole number that divides another number exactly, leaving no remainder.
The factors of 4 are 1, 2 and 4. That is three factors, which is an odd number, and in a moment you will see why that happens.
Factor Pairs of 4
Instead of testing every number, look for pairs that multiply to 4 and work from the outside in.
- Start with 1 × 4. Every number has this pair.
- Try 2. Since 4 ÷ 2 = 2, write 2 × 2.
- Try 3. It does not divide 4, and anything after 2 is already covered, so you are done.
Why 4 has an odd number of factors
Factors usually come in twos, one partner for each. But in 2 × 2 the partners are the same number, so 2 is only listed once. A number that behaves like this is a perfect square, and 4 is the first one after 1.
Prime Factorization of 4
Prime factors show what a number is built from. Split 4 into two numbers that multiply to it, and check whether each is prime.
So 4 = 2 × 2 = 2². The only prime factor of 4 is 2. Adding 1 to the exponent gives 2 + 1 = 3, which matches the three factors we found.
Is 4 a Prime or Composite Number?
Composite. A prime has just two factors, but 4 has three. In fact 4 is the smallest composite number, because 2 and 3 are both prime and 4 is the very next whole number.
Real-Life Uses of the Factors of 4
- Quarters. A dollar has 4 quarters, so sharing it among 1, 2 or 4 people leaves no change behind.
- Seasons and sides. A year has 4 seasons and a square has 4 equal sides.
- Tables. A table for 4 seats pairs up neatly as 2 and 2.
Common Factors of 4 With Other Numbers
The factors of 6 are 1, 2, 3 and 6, so the common factors of 4 and 6 are 1 and 2, and the GCF is 2. You can use that to simplify 4/6: divide the top and bottom by 2 and you get 2/3.
Quick Practice
Which of these are factors of 4: 2, 3 or 4? Only 2 and 4. 4 ÷ 3 leaves 1. Now try 8 yourself and check it with the calculator.