# What are the factors of 40?

Apr 15, 2016

The factors are $1$, $2$, $4$, $5$, $8$, $10$, $20$, $40$

#### Explanation:

I find factors in pairs, It will look like more work than it is, because I will explain how I am doing these steps. I do most of the work without writing it down. I'll put the explanation in black in [brackets] and the answer in $\textcolor{b l u e}{\text{blue}}$.

I'll proceed by starting with $1$ on the left and checking each number in order until either I get to a number already on the right or I get to a number greater than the square root of 40.

$\textcolor{b l u e}{1 \times 40}$

[I see that 40 is divisible by 2, and do the division to get the next pair]

$\textcolor{b l u e}{2 \times 20}$

[Now we check 3. But 40 is not divisible by 3. I usually write a number before I check, so if a number is not a factor, I cross it out.]]

$\textcolor{b l u e}{\cancel{3}}$

[Now we need to check 4. Up above, we got $40 = 2 \times 20$ since $20 = 2 \times 10$, we see that $40 = 2 \times 2 \times 10 = 4 \times 10$]

$\textcolor{b l u e}{4 \times 10}$

[The next number to check is 5. We can either divide $40 \div 5$ to get $8$ or split up the $10$ in the last factor pair: $40 = 4 \times 10 = 4 \times 2 \times 5 = 8 \times 5$]

$\textcolor{b l u e}{5 \times 8}$

{Move on to 6. But 40 is not divisible by 6. -- 6 is not a factor of 40.

$\textcolor{b l u e}{\cancel{6}}$

[40 is not divisible by 7.]

$\textcolor{b l u e}{\cancel{7}}$

The next number, $8$, already appears on the list above (on the right).
For numbers greater than $8$ to be factors of $40$ they would have to be multiplied by something less than the $5$ we use in $8 \times 5 = 40$. We've already checked the smaller numbers, so we're done.

The factors are $1$, $2$, $4$, $5$, $8$, $10$, $20$, $40$