Divisibility Tests set 2

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.

Read More

Divisibility Tests set 1

Divisibility by 2 When the last digit of a number is either 0 or even, then the number is divisible by 2. For example 12, 84, 474, 1000 etc., are divisible by 2.

Divisibility by 3 When the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
For example 12345
                             1 + 2 + 3 + 4 + 5 = 15
    which is divisible by 3, so 12345 must be divisible by 3

Divisibility by 4 When the number made by last two-digits of a number is divisible by 4, then that particular number is divisible by 4.
        For example 4528 is divisible by 4 as the number made by its last two digits i.e., 28 is divisible by 4

Also the number having two or more zeroes at the end, is also divisible by 4.
        For example The numbers 1400, 136000, 7860000 etc., are divisible by 4 as they have two or more zeroes at the end.

Divisibility by 5 Numbers having 0 or 5 at the end are divisible by 5. For example 35, 1650, 14750 etc., are divisible by 5 as they have 0 or 5 at the end.

Divisibility by 6 When a number is divisible by both 3 and 2, then that particular number is divisible by 6 also. For example 18, 36, 720 etc., are divisible by 6 as they are divisible by both 3 and 2.

Divisibility by 7 A number is divisible by 7 when the difference between twice the digit at ones place and the number formed by other digits is either zero or a multiple of 7.
           For example 658 is divisible by 7
because 65 -2 X 8 = 65 -16 = 49. As 49 is divisible by 7, the number 658 is also divisible by 7.

Read More