Two-digit divisor in long division

When the divisor has two digits, the procedure works the same way but instead of using facts from multiplication tables when dividing, we might have to use pencil and paper to perform helping multiplications on the side, so to speak.



14	7	4	3	4

14 goes into 7 zero times, so we look at 74. To find how many times does 14 go into 74, you probably have to do several guesses. Check until you find the maximum number of times that 14 goes into 74.

2 × 14 = 28
4 × 14 = 56

5 × 14 = 70
6 × 14 = 84

From this we can see that 14 goes into 74 five times.

			5

14		7	4	3	4
	-	7	0
			4	3

Now the question is how many times does 14 go into 43.

2 × 14 = 28
3 × 14 = 42
4 × 14 = 56,

so it is three times.

			5	3	1

14		7	4	3	4
	-	7	0
			4	3
		-	4	2
				1	4

At this point it is easy: how many times does 14
go into 14? That is exactly once, so the division
is exact and over.

1
531
× 14

2124
5310

7434

The check confirms our result.

Example problems

1. Divide using long division. Use the extra empty space for any multiplications you need to do. Finally check your division by multiplication.


15		8 7 6 0

× 15

When the divisor is a multiple of ten (that is, 20, 30, 40, etc.), the division is easier because it is easier to perform the helping multiplications.

		3

20	6	4	4	0

20 goes into 6 zero times, so we look at 64. We know that 3 × 20 = 60 and 4 × 20 = 80 so 20 goes into 64 three times.

			3	2

20		6	4	4	0
	-	6	0
			4	4

Now how many times does 20 go into 44? Again, answer is easy since 2 × 20 = 40 and 3 × 20 = 60.

			3	2	2

20		6	4	4	0
	-	6	0
			4	4
		-	4	0
				4	0

Lastly we know 20 goes into 40 exactly two times.

322
× 20

000
6440

6440

The check confirms our result.

2. Divide using long division. Do the divisions in your notebook, and record the results here. Remember to check each one by multiplication!

a. 9197 17 = ____ b. 9424 16 = ____
c. 1092 13 = ____
d. 2160 20 = ____

e. 3440 40 = ____ f. 9750 50 = ____
g. 6780 20 = ____
h. 4560 30 = ____

Divisibility rules

Do you remember?

Numbers that are divisible by 2 end in __, __, __, __, or __. Numbers that are divisible by 5 end in either __ or __.
Numbers that are divisible by 10 end in __ .

Division rule for 3 is different. No longer do we check in what the number ends:

If the sum of the digits of the number is divisible by 3, so is the number itself.

In other words, we add the digits of the number, and if that is divisible by 3, so is the original number.

Is 546 divisible by 3?	Yes, because 5 + 4 + 6 = 15, and 15 is divisible by 3.
Is 739 divisible by 3?	No, because 7 + 3 + 9 = 19, and 19 is not divisible by 3.

Example problems

1. Check if these numbers are divisible by three. Then divide the number by 3 in your notebook and record the answer here. What is the remainder if the number IS divisible by 3?

Number	sum of its digits	divisible by 3 (yes/no)	division result
771 8096 2304			771 ÷ 3 = ___, R ___ 8096 ÷ 3 = ___, R ___ 2304 ÷ 3 = ___, R ___

Division rule for 9 is similar to the division rule for 3.

If the sum of the digits of the number is divisible by 9, so is the number itself.

Is 546 divisible by 9?	No, because 5 + 4 + 6 = 15, and 15 is not divisible by 9.
Is 738 divisible by 9?	Yes, because 7 + 3 + 8 = 18, and 18 is divisible by 9.

2. Check if these numbers are divisible by nine. Then divide the number by 9 in your notebook and record the answer here. What is the remainder if the number IS divisible by 9?

Number	sum of its digits	divisible by 9 (yes/no)	division result
771 1000 333			771 ÷ 9 = ___, R ___ 1000 ÷ 9 = ___, R ___ 333 ÷ 9 = ___, R ___

3. Use the divisibility rules and check if the number is divisible by 2, 3, 5, or 9.

divisible by					divisible by
Number	2	3	5	9	Number	2	3	5	9
238 6095					477 5770

Division rule for 6 says

If the number is divisible by 2 and by 3, it is divisible by 6.

4. Check if these numbers are divisible by six. If it is, then divide the number by 6 in your notebook and record the answer here.

Number	divisible by 6 (yes/no)	division result
771 8196 1000		771 ÷ 6 = ___, R ___ 8196 ÷ 6 = ___, R ___ 1000 ÷ 6 = ___, R ___

5. a) Find two numbers that are divisible by both 10 and 3.
b) Find two numbers that are divisible by both 2 and 9.
More books about long division for kids

Mathimagination Series: Book A, beginning multiplication and division; Book B, operations with whole numbers; Book C, number theory, sets and number bases; Book D, fractions; Book E, decimals and percent

Decimals and Percentages With Pre- And Post-Tests: Place Value, Addition, Subtraction, Multiplication, Division

Read more