Division has existed for thousands of years. Ever since humans developed the ability to count and measure, or at least estimate size and quantity, division has existed. Food and produce would be divided up into absolute equality or, by the group's hierarchical structure. For example, much like a wolf pack, the person on the dominance hierarchy may take the largest portion of food or produce. Or the group could split food and produce into equal portions between everyone.

The earliest recorded instances of basic math date back 35,000 to 20,000 years in Africa. Bone and wood artefacts show that notches in these instruments were used to count. Ancient Babylonians and Ancient Egyptians used division. These were two of the first known civilizations in human history. This shows just how important and just how long division has been used to help human societies excel.

Division continued to evolve into more accurate calculations in Europe. The division symbol itself was first used in 1659, by the Swiss mathematician Johann Heinrich Rahn. This article will guide you through the divisibility rules.

Divisibility rules are a selection of math rules used to determine if a number is divisible by another specific number or not. These rules allow people to discover the factors and multiples of numbers without having to do long division.

In essence, a divisibility rule is a division shortcut. They allow people to quickly work out if an integer is divisible by a divisor. An integer that divides a number completely without a remainder is a divisor. Using a divisibility rule you can quickly examine digits to work this out, instead of going through the whole division process.

You can apply multiple divisibility rules to the same number to find out its prime factorization. Firstly there is no divisibility rule 1, as every number is divisible by 1 rendering rule 1 obsolete.

### What is divisibility rule 2?

The second divisibility rule allows you to see if a number is divisible by 2. This is a simple rule. All you have to do is check if the digit or the last digit ends in a zero or an even number. If this is the case then it is divisible by 2. If not then it is not divisible by 2.

### What is divisibility rule 3?

A number is divisible by 3 if the sum of all the digits is divisible by 3. For example, if you had the number 156 you would add all those numbers together. This would give you the number 12. If you divide this number by 3 you get 4 with no remainder. Therefore, 156 is divisible by 3.

### What is divisibility rule 4?

A number is divisible by 4 if the last two digits form a number that is divisible by 4. For example, the number 3532 is divisible by 4. This is because the last two digits are 32, and 32 is divisible by 4, which equals 8.

### What is divisibility rule 5?

The fifth rule is one of the easier rules to follow. Any number that ends in zero or 5 is divisible by 5. For example, the number 650 is divisible by 5, which equals 130.

### What is divisibility rule 6?

A number is divisible by 6 if it is divisible by 2, and it is also divisible by 3. So, for example, if you have the number 606 it is divisible by 6. This is because it is divisible by 2 as it ends in an even number.

Also, if you add the digits together it gives you a total of 12. Therefore, the total number is divisible by 3, because 12 divided by 3 equals 4 with no remainder. So, 606 is divisible by 6 as it is also divisible by 2 and 3.

### What is divisibility rule 7?

To work out if a number is divisible by 7 you need to double the last number. Then you subtract this number from the remaining number. If that figure is either zero or is divisible by 7 the entire number is divisible by 7.

Using 196 as an example number, you double the last digit to equal 12. The remaining digits are 19. Then 19 minus 12 is 7. The number 7 can be divided by 7, to give 1, which means the entire number is divisible by 7.

### What is divisibility rule 8?

An entire number is divisible by 8, if the last three digits are divisible by 8. For example, the number 3600 is divisible by 8. This is because the last three digits (600) can be divided by 8 to give 75. So, because the last three digits are divisible by 8, 3600 is divisible by 8.

### What is divisibility rule 9?

A number is divisible by 9 if the sum of the digits is divisible by 9. So, using 297 as an example, you will add, 2 + 9 + 7 which equals 18. The number 18 can then be divided by 9 which equals 2. So because the sum of all digits is divisible by 9 the entire number is divisible by 9.

### What is divisibility rule 10?

This is perhaps the easiest rule to follow as no problem solving is required. Simply, if a number ends in a zero the number is divisible by 10. As the difficulty ramps up after rule 10, many people only teach divisibility rules from 1 - 10. However, many sources teach divisibility rules from 1- 13. So, we will continue to rule 13, but you may prefer only to use 1 - 10 if you are not confident in your math skills.

### What is divisibility rule 11?

In order to work out if a number is divisible by 11, you will add all of the even-placed digits together. You will also add all of the odd-placed numbers together. You then subtract the sum of the digits in equal places by the sum of the digits in odd places. If that given number is divisible by 11, the whole number is also divisible by 11.

For example, if your starting number is 451 that number is divisible by 11. This is because the even placed sum is 5, and the odd placed number sum is 5, (4 + 1). So, 5 minus 5 is zero, which is divisible by 11.

### What is divisibility rule 12?

For a number to be divisible by 12 it must be divisible by 3 and also divisible by 4. The number 132 is an example of this. This is because the sum of the digits 132 equals 6. So, because 6 is divisible by 3, equaling 2, 132 is divisible by 3.

The number 132 is also divisible by 4. This is because when you divide the last two digits (32) by 4 you get 8. Therefore, because 132 is divisible by 3 and divisible by 4 it is also divisible by 12.

### What is divisibility rule 13?

To work out if a number is divisible by 13 you will first need to multiply the last digit by 9. You will then subtract this number by the remaining number. The number 247 is an example of a number divisible 13.

Using rule 13 you will multiply 7 by 9, which gives the figure 63. The number 24 is left in the number sequence. So, 24 minus 63 is -39. The whole number is divisible by 13 because -39 is divisible by 13.

### What is the quickest way to divide a number?

Although it is always good to know divisibility rules in case you do not have a calculator or internet connection, there is an easier way. An online division calculator will do all the legwork for you. All you need is an internet connection and a device to access the website.

Simply enter the number you want to calculate and the number you want to divide it by into the number boxes. Then press calculate to get an accurate division number.

Mathematics has existed for tens of thousands of years. The first recorded instances of math were bones and pieces of wood with notches scraped into them to count. In terms of division, calculations have dated back to at least Ancient Egypt and Ancient Babylon. It was used to help divide stock and goods in trade.

A number of divisibility rules are used as a shortcut to find out if a number is divisible by another number. This is without having to go through the entire mathematical process. The divisibility rules 2 - 13 are shown in detail above. There is no rule 1 as every number is divisible by 1.

However, you can also use an online division calculator for the fastest most efficient way to divide a number.