Chapter 14
LONG DIVISION BY FACTORS
Most people don’t mind short division (or simple division) but they feel uneasy when it comes to long
division. To divide a number by 6 you need to know your 6 times table. To divide a number by 7, you
need to know your 7 times table. But what do you do if you want to divide a number by 36? Do you
need to know your 36 times table? No, not if you divide using factors.
What Are Factors?
What are factors? We have already made use of factors when we used 20 as a reference number with
our multiplication. To multiply by 20, we multiply by 2 and then by 10. Two times 10 equals 20. We are
using factors, because 2 and 10 are factors of 20. Four and 5 are also factors of 20 because 4 times 5
equals 20.
Just as we made use of factors in multiplication, we can use factors to make long division easy. Let’s
try long division by 36.
What can we use as factors? Four times 9 is 36, and so is 6 times 6. We could also use 3 times 12.
Let’s try our calculation using 6 times 6.
We will use the following division as an example:
2,340 ÷ 36 =
We can set out the problem like this:
Or like this:Use the layout that you are comfortable with.
Now, to get started we divide 2,340 by 6. We use the method we learnt in the previous chapter.
We begin by dividing the digit on the left. The digit on the left is 2, so we divide 6 into 2. Two is less
than 6 so we can’t divide 2 by 6, so we join 2 to the next digit, 3, to make 23.
What number do we multiply by 6 to get an answer of 23? There is no whole number that gives you
23 when you multiply it by 6. We now ask, what will give an answer just below 23? Three times 6 is 18.
Four times six is 24, which is too high, so our answer is 3. Write 3 below the 3 of 23. Subtract 18 (3 ×
6) from 23 to get an answer of 5 for our remainder. We carry the 5 remainder to the next digit, 4,
making it 54. Our work so far looks like this:
We now divide 6 into 54. What do we multiply by 6 to get an answer of 54? The answer is 9. Nine
times 6 is exactly 54, so we write 9 and carry no remainder.
Now we have one digit left to divide. Zero divided by 6 is 0, so we write 0 as the final digit of the
first answer. Our calculation looks like this: