Division - How to know if a number divides evenly without a remainder

To know if a number is divisible by one, there is actually no need to remember anything because any number divided by 1 will give you the same number you wanted to divide in the first place, so in other words - every number (except zero) is divisible by 1.

If the number you want to divide is an even number, it will always be divisible by two and give us a whole number.

For example:

• 2/2=1
• 5844/2=2922
• 26/2=13
• 228/2=114
• 10/2=5

When we have small numbers, it's very easy to know if they are divisible by 3 because we learned the multiplication table

• 9/3=3
• 12/3=4
• 21/3/7

It's very simple to know if a long number is divisible by 3 if you add up its digits and then check if the resulting number is divisible by 3

For example: Is the number 1071 divisible by three? Let's see

1+0+7+1=9

9/3=3

So indeed, the number 1071 is divisible by three. Let's try another number, and this time let's take a longer number, say: 23457

2+3+4+5+7=21

21/3=7

Simple, right?

To know if a number is divisible by 4 "nicely", you just need to know if it's divisible by 2 twice

For example:

• 16/2=8
• 8/2=4

From this we understand that the number 16 is indeed divisible by 4 and the result will be 4.

Let's take another number. Let's say 22. Is the number 22 divisible by 4? Let's check

• 22/2=11
• 11/2=5.5

The result we got is 5.5, from this we understand that the number 22 does not divide evenly by 4.

Division by 5 is one of the easy things to remember. All we need to know is that any number ending in 5 or 0 (except for the digit zero itself) is indeed divisible by 5.

For example:

• 15/5=3
• 90/5=18
• 221565/5=44313
• 9876543210=1975308642

To know if a certain number is divisible by six, the simplest way is to check if it is an even number and if it is also divisible by 3

For example:

• 36/2=13
• 36 - 3+6=9/3=3

In the number 36 for example, we see that it is an even number since its last digit is 0,2,4,6 or 8 and indeed we see that it is divisible by 2 and it is also divisible by 3, therefore 36 is definitely divisible by 6

The number seven is a more "tricky" number but there is a method to know if it divides by 7 without a remainder by removing the ones digit from the number, and then subtracting from the remaining number the ones digit that was removed multiplied by 2.

For example:

• We have the number 196.
• We remove its ones digit and are left with 19
• Then we multiply the ones digit we removed and got 6*2=12
• Now we have to subtract 19-12=7. From this we can conclude that the original number - 196 is indeed divisible by 7.

Let's try another example with a scarier number: 1099.

• Let's review the process. We separate the ones digit 9 (and remember its product by 2 which is 18)
• Then we subtract it from the number remaining without the ones digit: 109-18=91
• Is 91 divisible by 7? Definitely. We know this from the multiplication table. 91/7=13

Similar to what we explained about division by 4, we do the same with eight, except this time we need the number to be divisible by 2 three times and give us a whole result, without a remainder

For example:

• 8/2=4
• 4/2=2
• 2/2=1

Therefore the digit eight (of course) is divisible by 8. Now let's try with a larger number for demonstration: 1320

• 1320/2=660
• 660/2=330
• 330/2=165

Therefore, the number 1320 is also divisible by 8

To know if a number is divisible by nine, there is a particularly fun trick. Here there is no need to do special calculations, but rather all you need to do is sum all the digits in the number.

For example:

• 14112
• 1+4+1+1+2=9

• 99
• 9+9=81
• 8+1=9

• 1114713
• 1+1+1+4+7+1+3=18
• 1+8=9

Knowing whether a number is divisible by ten is perhaps the easiest thing to remember - does the number end with 0? If so, then it will always be divisible by 10, and all you need to do for the answer is remove the ones digit, which is the zero digit, and you have your answer.

• 100/10=10
• 50/10=5
• 78536544915750/10=7853654491575

Any number you try to divide by zero will give you an undefined result.

Division is actually multiplication by a reciprocal number. For example, $10\over5$ equals $10\cdot1 \over 5$. Since zero has no reciprocal number, it's simply impossible to divide any number by zero.

1. Which of the following numbers are divisible by two?

• 132
• 96
• 56874
• 555
• 778

2. Which of the following numbers are divisible by three?

• 18
• 65435
• 210
• 12345
• 666

3. Which of the following numbers are divisible by four?

• 64
• 162
• 4096
• 1112
• 3336

4. Which of the following numbers are divisible by five?

• 555
• 5687
• 123
• 100
• 5050506

5. Which of the following numbers are divisible by six?

• 18
• 72
• 3582
• 82
• 480

6. Which of the following numbers are divisible by seven?

• 98
• 56
• 1535
• 887
• 777

7. Which of the following numbers are divisible by eight?

• 64
• 326
• 16384
• 865221
• 65536

8. Which of the following numbers are divisible by nine?

• 45
• 82
• 315
• 4555
• 41112

9. Which of the following numbers are divisible by ten?

• 654210
• 2154
• 642185
• 13220
• 100000000000