# Playing with Numbers – Chapter 3

CBSE CLASS 6 MATHEMATICS
Playing With Numbers – Chapter 3
Tests for Divisibility of Numbers:

Divisibility by 10:
If a number has 0 in the ones place then it is divisible by 10.
Examples: 1000, 3200, 7010……

Divisibility by 5:
A number which has either 0 or 5 in its ones place is divisible by 5.
Examples: 105, 3500, 1750125…….

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.
Examples: 2410, 4356, 1358, 2972, 5974…………………

Divisibility by 3:
If the sum of the digits is a multiple of 3, then the number is divisible by 3.
Examples: 219, 1089, 90756 ……..
Sum of the digits = 2+1+9 =12, which is a multiple of 3.So 219 is divisible by 3.
Sum of the digits = 1+0+8+9=18, which is a multiple of 3. So 1089 is divisible by 3.
Sum of the digits = 9+0+7+5+6 = 27, which is a multiple of 3. So 90756 is divisible by 3.

Divisibility by 6:
If a number is divisible by 2 and 3 both then it is divisible by 6 also.
Examples: 297144, 639210, 1790184……..
All these numbers are even numbers. So it is divisible by 2.
Now check the divisibility by 3.
Sum of the digits = 2+9+7+1+4+4 = 27, which is a multiple of 3.
So 297144 is divisible by 6 also.

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.
Examples: 212, 1936, 9532 ………………
In the above examples, last two digits are 12, 36, 32 ……
All these numbers are divisible by 4, so 212, 1936, 9532…………… is divisible by 4 also.

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.
Examples: 10216, 73512, 24416……
In the above examples last three digits are 216, 512, 416 …..
All these numbers are divisible by 8, so10216, 73512, 24416………… is divisible by 8.

Divisibility by 9:
If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.
Examples: 4608, 5283, 4320927……
Sum of the digits = 4+6+0+8 = 18, which is divisible by 9.
Sum of the digits = 5+2+8+3 = 18, which is divisible by 9.
Sum of the digits = 4+3+2+0+9+2+7 = 27, which is divisible by 9.
So all these numbers are divisible by 9.

Divisibility by 11:
The rule is, find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11.
Examples: 308, 1331, 61809……………….
1. Sum of the digits at odd places = 8+3 = 11
Sum of the digits at even places = 0
Difference = 11-0 = 11, which is divisible by 11.
So 308 is divisible by 11.
2. Sum of the digits at odd places = 1+3 = 4
Sum of the digits at even places = 3+1 = 4
Difference = 4 – 4 =0, which is divisible by 11.
So 1331 is divisible by 11.
3. Sum of the digits at odd places = 9 +8+6 = 23
Sum of the digits at even places = 0+1 = 1
Difference = 23 – 1 = 22, which is divisible by 11.
So 61809 is divisible by 11.