The document discusses tests for divisibility of numbers by single-digit numbers from 2 to 11. It states that a number is divisible by 2 if its ones place contains an even digit (0, 2, 4, 6, 8). A number is divisible by 3 if the sum of its digits is divisible by 3. For divisibility by 4, the last two digits must be divisible by 4. A number is divisible by 5 if its ones place is 0 or 5. A number is divisible by 6 if it is divisible by both 2 and 3. For divisibility by 8, the sum of the last three digits must be divisible by 8. A number is divisible by 9 if the sum of its digits is divisible by 9

1. TESTS FORTESTS FOR
DIVISIBILITY OFDIVISIBILITY OF
NUMBERNUMBER

2. Divisibility by 2Divisibility by 2
A number is divisible by 2A number is divisible by 2
if it has any of the digits-if it has any of the digits-
0,2,4,6,8 in the ones pace0,2,4,6,8 in the ones pace

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

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

5. Divisibility by 5Divisibility by 5
A number which has eitherA number which has either
0 or 50 or 5
Ni its ones place is divisibleNi its ones place is divisible
by 5.by 5.

6. Divisibility by 6Divisibility by 6
if the number is divisible by 2 orif the number is divisible by 2 or
3 both then it is divisible by 63 both then it is divisible by 6
alsoalso

7. Divisibility by 8Divisibility by 8
A number with 4 or moreA number with 4 or more
digits is divisible by 8 , if thedigits is divisible by 8 , if the
number formed by the lastnumber formed by the last
three digits is divisible by 8.three digits is divisible by 8.

8. Divisibility by 9Divisibility by 9
If the sum of the digits of aIf the sum of the digits of a
number is divisible by 9,number is divisible by 9,
then the number itself isthen the number itself is
divisible by 9.divisible by 9.

9. Divisibility by 10Divisibility by 10
Divisibility by 10 –Divisibility by 10 –
If a number has 0 in the ones placeIf a number has 0 in the ones place
Then it is divisible by 10Then it is divisible by 10

10. Divisibility by 11Divisibility by 11
Find the difference between the sumFind the difference between the sum
of the digits at odd placesof the digits at odd places
(from the right) and the sum of the(from the right) and the sum of the
Digits at even place (from the right) ofDigits at even place (from the right) of
the number . If the difference is eitherthe number . If the difference is either
0 or divisible by 11,then the number is0 or divisible by 11,then the number is
divisible by 11.divisible by 11.

11. Have Nice Day
Made By:-
Harshit Pancholi