3.3 Prime factorization of natural numbers

3 is a factor of 27, since $\text{27}÷3=9$ , or $3\cdot 9=\text{27}$ .

7 is a factor of 56, since $\text{56}÷7=8$ , or $7\cdot 8=\text{56}$ .

4 is not a factor of 10, since $\text{10}÷4=\mathrm{2R2}$ . (There is a remainder.)

Find all the factors of 24.

$\begin{array}{ccc}\text{Try 1:}\hfill & \text{24}÷1=\text{24}\hfill & \text{1 and 24 are factors}\hfill \\ \text{Try 2:}\hfill & \text{24 is even, so 24 is divisible by 2.}\hfill & \\ & \text{24}÷2=\text{12}\hfill & \text{2 and 12 are factors}\hfill \\ \text{Try 3:}\hfill & 2+4=6\text{and 6 is divisible by 3, so 24 is divisible by 3.}\hfill & \\ & \text{24}÷3=8\hfill & \text{3 and 8 are factors}\hfill \\ \text{Try 4:}\hfill & \text{24}÷4=6\hfill & \text{4 and 6 are factors}\hfill \\ \text{Try 5:}\hfill & \text{24}÷5=\mathrm{4R4}\hfill & 5\text{ is not a factor.}\hfill \end{array}$

The next number to try is 6, but we already have that 6 is a factor. Once we come upon a factor that we already have discovered, we can stop.

All the whole number factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.