CBSE & NCERT Class 6 Maths Divisibility of Numbers and Test of Divisibility

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 128 divisible by 2, 128÷2=64 Yes(exactly)

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

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 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

1312 is (12÷4=3) Yes(exactly)

7019 is not (19÷4=4 ³/₄) No(the result is not a whole number)

A Useful trick for small numbers- Halve 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 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

175 = 175÷5=35 Yes(exactly)

809 = 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 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 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 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

109816 (816÷8=102) Yes(exactly)

216302 (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 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 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.

For more such articles, demos for Test of Divisibility, worksheets for Class 6 Maths, NCERT Solutions of Class 6 and other classes please login at www.takshilalearning.com

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