**Divisibility Rules From 2 to 10 – CBSE & NCERT Class 6 Maths**

Test of Divisibility – Takshila Learning objective is to help build Class 6 students build a strong foundation in Mathematics. Mathematical concepts have been introduced and explained through Animated videos, activities and real-life situations ranging from the concrete to the abstract. Explore our collection of **CBSE 6 Class Maths**. In this article, we share ‘Test of Divisibility’.

“Divisible By “means ” when you divide one number by another the result is a whole number”

Examples:

12 **is** divisible by 4 because 12 ÷ 4= 3 (**exactly)**

15 is **not** divisible by 4 because 15 ÷ 4 =** 3.75**(the result is **not** a whole number)

0 **is** divisible by 4 because 0 ÷ 4 = 0 **exactly** (0 is a whole number)

**The Divisibility Rules – 2 to 10**

There are many tricks or shortcuts that allow testing whether a number or dividend, is divisible by a given divisor.The Divisibility rules help you to test if one number is divisible by another, without too much calculation and in less time!

**Divisibility Rule of 2**

** Divisibility by 2**: A number is divisible by 2 if it has any of the digits 0,2,4,6, or 8 in its ones place.

Let’s check

Is 12**8** divisible by 2, 128÷2=64 **Yes**(exactly)

Is 12**9** divisible by 2, 129÷2 = 64.5 **No**(the result is **not** a whole number)

**Divisibility Rule of 3**

** Divisibility by 3:**If the sum of the digits is a multiple of 3, then the number is divisible by 3.

Let’s check

381 (3+8+1=12, and 12÷3 = 4) **Yes**(exactly)

217 (2+1+7=10, and 10÷3 = 3 ^{1}/_{3}) **No**(the result is **not** a whole number)

**This rule can be repeated whenthe number is greater than 3 digit:**

99996 (9+9+9+9+6 = 42, then 4+2=6) **Yes**(exactly)

**Divisibility Rule of 4**

** Divisibility by 4:**A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.

Let’s Check

13**12** is (12÷4=3) **Yes**(exactly)

70**19** is not (19÷4=4 ^{3}/_{4}) **No**(the result is **not** a whole number)

*A Useful** trick for small numbers- **H*alve the number twice and a result is still a whole number, then the number is divisible by 4.

12/2 = 6, 6/2 = 3, 3 is a whole number. **Yes**(exactly)

30/2 = 15, 15/2 = 7.5 which is not a whole number. **No**(the result is **not** a whole number)

**Divisibility Rule of 5**

** Divisibility by 5:**A number which has either 0 or 5 in its place is divisible by 5. The last digit is 0 or 5.

Let’s Check

17**5** = 175÷5=35 **Yes**(exactly)

80**9** = 809÷5=161.5 **No**(the result is **not** a whole number)

For a detailed explanation with examples are available at *CBSE Class 6 Maths online classes*

**Divisibility Rule of 6**

** Divisibility by 6:** If a number is divisible by 2 and 3 both then it is divisible by 6 also.

114 (it is even, and 1+1+4=6 and 6÷3 = 2) **Yes**(exactly)

308 (it is even, but 3+0+8=11 and 11÷3 = 3 ^{2}/_{3}) **No**(the result is **not** a whole number)

**Divisibility Rule of 7**

** Divisibility by 7:**Double the last digit and subtract it from a number made by the other digits. Then it will be divisible by 7.

672 (Double 2 is 4, 67-4=63, and 63÷7=9) **Yes**(exactly)

105 (Double 5 is 10, 10-10=0, and 0 is divisible by 7) **Yes**(exactly)

905 (Double 5 is 10, 90-10=80, and 80÷7=11 ^{3}/_{7}) **No**(the result is **not** a whole number)

**Divisibility Rule of 8**

** Divisibility by 8:** A number with 4 or more digits is divisible by 8 if the number formed by the last three digits is divisible by 8.

Let’s Check

109**816** (816÷8=102) **Yes**(exactly)

216**302** (302÷8=37 ^{3}/_{4}) **No**(the result is **not** a whole number)

** One more trick**– Halve three times the number and the result is still a whole number:

816/2 = 408, 408/2 = 204, 204/2 = 102 **Yes**(exactly)

302/2 = 151, 151/2 = 75.5 **No**(the result is **not** a whole number)

**Divisibility Rule of 9**

** Divisibility by 9:** If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.

Example

1629 (1+6+2+9=18, and again, 1+8=9)

1629÷9=181 **Yes**(exactly)

2013 (2+0+1+3=6)

2013÷9=223.66 **No**(the result is **not** a whole number)

**Divisibility Rule of 10**

** Divisibility by 10:**If a number has 0 in the one’s place then it is divisible by 10.

220÷10=22 **Yes**(exactly)

221÷10=22.1 **No**(the result is **not** a whole number)

*For Divisibility by 11, 12, and more is available at CBSE Class 6 Online Classes*

__Some more Divisibility rules__

- If a number is divisible by another number then it is divisible by each of the factors of that number.
- If a number is divisible by two co-prime numbers then it is divisible by their product also.
- If two given numbers are divisible by a number, then their difference is also divisible by that number.

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