Here is a handy **rules divisibility chart** that lists
all the divisibility rules

Divisibility is capable of being divided, especially with no remainder hen one number can be divided by another and the result is an exact whole number. Example: 15 is divisible by 3 because 15 : 3 = 5 exactly. But 9 is not divisible by 2 because 9 : 2 is 4 with 1 left over.

So we can make **rules of divisibility**.
By looking at numbers in a certain way or by using specific tricks
you can quickly check out the divisibility of numbers.
Now we wiil check out the divisibility by 2, 3, 4, 5, 6 ,7 ,8, 9 and 10.

The are specific rules of divisibility for each digit

- When the number is not 10 times bigger than the divisor, use your knowledge of the multiplications tables. So 47 is not 10 times bigger than 5. you know, using your multiplications tables, that 47 is not divisible by 5.
- When the number is more than 10 times bigger than the divisor you first reduce the numbers with multiples of 10 times the divisor and then use your multiplications tables for the remainder. So is 1447 divisible by 7? 1447 reduced with multiples of 10 times 7 (20 * 70 = 1400). The remainder 47 is not divisible by 7 so 1447 is not divisible by 7

**Divisibility by 2 rule**: The divisibility by 2 is easy: any number that ends in an even digit (0, 2, 4, 6, 8) is divisible by 2.- 215 doesn't end in 0,2,4,6 of 8 and is NOT divisible by 2
- 116 ends in 0,2,4,6 or 8 and is SURELY divisible by 2

**Divisibility by 3 proof**: Divisibility by 3 is simple: if the digit sum is divisible by 3, then the number is divisible by 3. The digit sum is the sum of the digits of a number.- 214 gives 2+1+4 = 7 and is NOT divisible by 3
- 159 gives 1+5+9 = 15 and is SURELY divisible by 3

**Divisibility by 4 test**: A number is divisible by 4 if the number's last two digits are divisible by 4.- 450 gives 50 and is NOT divisible by 4
- 840 gives 40 and is SURELY divisible by 4

There is another way to check the divisibility by 4. A number is divisible by 4 if the last 2 digits can by divided twice by 2 (128 is divisible by 4 because 28 : 2 = 16 and 16 : 2 = 8). or a number is divisible by 4 if the last two digits can be divided by 2 and gives you and even number.

**Divisibility by 5 rule**: The divisibility by 5 is a very easy divisibility rule. If the last digit is zero or 5, then the number is divisible by 5.- 714 doesn't end in 0 or 5 and is NOT divisible by 5
- 150 ends in 0 and is SURELY divisible by 5
- 675 ends in 5 and is SURELY divisible by 5

**Divisibility by 6 proof**: The test the divisibility by 6 you'll haven to know the divisibility by 3 rule. Any even number that is divisible by 3 is also divisible by 6.- 713 is uneven and so NOT divisible by 6
- 152 is even, but 1+5+2=8 and is NOT divisible by 3.

So 152 and is NOT divisible by 6 - 474 is even and 4+7+4= 15 and is divisible by 3

So 474 is SURELY divisible by 6

**Divisibility by 7 test**: a) Chop off the ones digit and double it.

b) Compare that product with the new number that is formed without the digit you’ve chopped off.

c) If the numbers are equal, the original number is divisible by 7; if not subtract the smaller number from the larger number. If the difference is divisible by 7, then the original number is divisible by 7. d) If you are not sure if the difference from step c is divisible by 7, repeat steps a-c. You may repeat steps a-c until the difference is a one-digit number.- 182 is SURELY divisible by 7 because 18-4=14 and 14 is SURELY divisible by 7
- 273 is SURELY divisible by 7 because 27-6=21 and 21 is SURELY divisible by 7
- 465 is NOT divisible by 7 because 46-10=36 and 36 is NOT divisible by 7

**Divisibility by 8 rule**: A number passes the divisibility by 8 test if the last three digits form a number that is divisible by 8. To make it easier you can first reduce the number with a maximum of multiples of 10 times 8. So with 1942 you check 22- 397 is NOT divisible by 8 because 397-360 (max multiples) gives 37 and 37 is NOT divisible by 8
- 2192 is SURELY divisible by 8 because 192-160 (max multiples) gives 32 and 32 is SURELY divisible by 8

**Divisibility by 9 proof**: If the digit sum is divisible by 9, then the number is divisible by 9.- 211 gives 2+1+1 = 4, and is NOT divisible by 9
- 684 gives 6+8+4 = 18 and is SURELY divisible by 9

**Divisibility by 10 test**: Any number ending in zero is divisible by 10- 841 is NOT divisible by 10 because the last digit is 1
- 730 is SURELY divisible by 10 because the last digit is 0.

The knowledge of the rules of divisibility can help you quickly determine whether a number is divisible by a certain number. The rules of divisibility are very handy when you are reducing fractions. Simplifying fractions makes use of the divisibility of numbers.