What Are the Factors of 16?
Line up 16 tiles and you can make a long strip of 16, a block of 2 by 8, or a perfect 4 by 4 square. Each of those shapes is a factor at work. A factor is a whole number that divides another number exactly, with no remainder.
The factors of 16 are 1, 2, 4, 8 and 16. That is five factors, an odd number, because 16 is a perfect square.
Factor Pairs of 16
Look for pairs that multiply to 16, from the outside in.
- Start with 1 × 16.
- Try 2. Since 16 ÷ 2 = 8, write 2 × 8.
- Try 3. It leaves a remainder, so skip it.
- Try 4. Since 16 ÷ 4 = 4, write 4 × 4. The partners match, so you are done.
Prime Factorization of 16
Prime factors show what 16 is built from. Split it and keep going until every branch is prime.
So 16 = 2 × 2 × 2 × 2 = 2⁴. Add 1 to the exponent, 4 + 1 = 5, and that is your factor count.
Why 16 is a perfect square
Since 4 × 4 = 16, the square root of 16 is exactly 4. That repeated pair is why the factors are odd in number.
Is 16 a Prime or Composite Number?
Composite. It has five factors. The sum of the factors is 1 + 2 + 4 + 8 + 16 = 31.
Real-Life Uses of the Factors of 16
- Ounces. A pound is 16 ounces, so half, a quarter and an eighth of a pound are all whole ounces.
- Computing. Hexadecimal counts in base 16, and memory is built from doubling steps.
- Grids. A 4 by 4 board has 16 squares.
Common Factors of 16 With Other Numbers
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24, so 16 and 24 share 1, 2, 4 and 8. The GCF is 8, which turns 16/24 into 2/3.
Quick Practice
Which of these are factors of 16: 4, 6 or 8? That is 4 and 8. Now try 32 and check it with the calculator.