Divisibility by 8 When the number made by last three digits of a number is divisible by 8, then the number is also divisible by 8
For example 2256 As 256 (the last three digits of 2256) is divisible by 8, therefore 2256 is also divisible by 8.Also if the last three or more digits of a number are zeroes, then the number is divisible by 8
For example 2462000 As 2462000 has three zeroes at the end. Therefore it will definitely divisible by 8
Divisibility by 9 When the sum of all the digits of a number is divisible by 9, then the number is also divisible by 9. For example (i) 936819 9+3 + 6 + 8 + 1 + 9= 36 which is divisible by 9. Therefore, 936819 is also divisible by 9.
Divisibility by 10 When a number ends with zero, then it is divisible by 10. For example 20, 30, 120, 26870 etc., are divisible by 10 as these all end with zero.
Divisibility tests set 1
Divisibility by 11 When the sums of digits at odd and even places are equal or differ by a number divisible by 11, then the number is also divisible by 11.
For example (i) 2865423
Let us see
Sum of digits at odd places (A) = 2 + 6+4 + 3 = 15
Sum of digits at even places (B) = 8 + 5 + 2 = 15
=>A = B Hence, 2865423 is divisible by 11.
ii) 217382
Let us see
Sum of digits at odd places (A) = 2 + 7 + 8 = 17
Sum of digits at even places (B) = 1 + 3 + 2 = 6
Now A- B = 17-6 = 11
Clearly, 217382 is divisible by 11.
Divisibility by 12 A number which is divisible by both 4 and 3 is also divisible by 12. For example 2244 is divisible by both 3 and 4. Therefore, it is divisible by 12 also.
Divisibility by 14 A number which is divisible by both 7 and 2 is also divisible by 14. For example 1232 is divisible by both 7 and 2. Therefore, it is divisible by 14 also.
Divisibility by 15 A number which is divisible by both 5 and 3 is divisible by 15 also. For example 1275 is divisible by both 5 and 3. Therefore, it is divisible by 15 also.
