**What is Divisible?**

In Mathematics, a number is said to be divisible by another number is said to be divisible if it does not produce a remainder. That means when you divide the two numbers, the remainder should be a 0. You can tell if a number is divisible by something by checking whether it meets the divisibility rules. These are set of rules that help people know whether a number is divisible by another number without carrying out the division.

**Divisibility Rules 1- 20**

**1.** Any number is divisible by 1. Because when you divide any number by 1, you will always get the number itself.

**For example 64 ¸ 1 = 64**

**2.** A number is divisible by 2 if it’s an even number or ends with 0, 2, 4, 6, and 8.

** For example 248 ****¸ 2 = 124**

**3.** A number is divisible by 3 if the total sum of its digits is divisible by 3

For Example 282 is divisible by 3 because 2 + 8 + 2 = 12.

** 282 ****¸ 3 = 94**

**4.** A number is divisible by 4 if its last two digits are divisible by 4

**For Example, 964 is divisible by 4 because 64 is divisible by 4**

**964 ****¸ 4 = 241**

**5.** A number is divisible by 5 if the last digit ends with a Zero or a 5

**For example, 1085 is divisible by 5 because the last digit is a 5**

**1085 ****¸ 5 = 217**

**6.** A number is divisible by 6 if it’s divisible by both numbers 2 and 3

For example, 90 is divisible by 6 since it’s divisible by 2 and 3

**90 ****¸ 2 = 45**

**90 ****¸ 3 = 30 **

**90 ****¸ 6 = 15**

**7.** A number is divisible by 7 if the difference between twice its unit digits from the remaining part is a 0 or a multiple of 7

**For example, 574 is divisible by 7 because 57- 8 =49 (49 is a multiple of 7)**

**8.** A number is divisible by 8 if the last 3 digits are divisible by 8

**For example: 600, 256 is divisible by 8 because 256 is divisible by 8. But 90, 413 is not divisible by 8 because 513 is not divisible by 8.**

**9.** A number is divisible by 9 if the sum of its digits is divisible by 9

**For example, 909 is divisible by 9 because 9 +0 +9 =18 (18 is divisible by 9)**

**10.** A number is divisible by 10 if its last digit is a 0

**For Example, 10, 20, 30, 40, 50, 60, 70**

**11.** A number is divisible by 11 if the difference of its sums of alternating digits from left to the right is divisible by 11 or it’s a 0

**For example 2849 is divisible by 11 because: 2+4 = 6, 8+9=17 >> 17-6= 11**

**12. **A number is divisible by 12 if it can be divided by both 3 and 4

**For example 36 is divisible by 12 because 36 ****¸ 4 = 9 and 36 ****¸ 3 = 12 **

**13.** A number is divisible by 13 if the number at the one’s position can be multiplied by 4 and then added to the rest to produce a multiple of 13 or a 0

For example, 3367 is divisible by 13 because;

**7 ****× 4= 28**

**336 +28 = 364**

**364 is a multiple of 13 (13 ****× 28 =364) **

**14.** A number is divisible by 14 if it can be divided by both 7 and 2

**For example, 84 is divisible by 7 because**

**84 ****¸ 7 = 12**

**84 ****¸2 = 42**

**15. **A number is divisible by 15 if it’s divisible by both 3 and 5

**For example, 90 is divisible by 15 because**

**90 ****¸ 5 = 18**

**90 ****¸ 3 = 30 **

**16.**** **A number is divisible by 16; if the last two digits are added four times, the remaining numbers result in a number divisible by 16.

**For example 1168 is divisible by 16 because**

**68 + (11 ****× 4) = 112 (112 is divisible by 16)**

**17. **A number is divisible by 17 if subtract the last two digits from two times the rest and produces a number divisible by 17

**For example 4675 is divisible by 17 because:**

** 46 ****× 2 – 75 = 17**

**18. **A number is divisible by 18 if it can be divided by both 2 and 9

**For example, 180 is divisible by 18 because**

**180 ****¸ 2 = 90 **

**180 ****¸ 9 =20**

**19.** A number is divisible by 19 if you add 4 times the last two digits to the remaining, and the answer is divisible by 19

**For example 6935 is divisible by 19 because 69 +35 ****× 4 =209. **

**20. **A number is divisible by 20 if it’s divisible by 4 and 5 or if the last two digits form a number that is divisible by 20** **

**For example, 220 is divisible by 20 because **

**220 ****¸ 5 = 44**

**220 ****¸ 4 = 55**