Day 2 Chapter 1 TEST OF DIVISIBILITY

Test of Divisibility

1. Divisibility By 2: A number is divisible by 2, If its unit digit is any of 0, 2, 4, 6, 8

Ex: 876456 is divisible by 2, while 987345 is not.

2. Divisibility by 3: A number is divisible by 3, If the sum of its digits is divisible by 3 or If the sum of the digits is equal to 3, 6, 9.

Ex: 592482 is divisible by 3, since the sum of the digits is 3.

3. Divisible by 4: A number is divisible by 4, if the number formed by last two digits of the number is divisible by 4.

Ex: 892648 is divisible by 4, since the last two digits are divisible by 4.

4. Divisible by 5: A number is divisible by 5, if its unit’s digit either 5 or 0.

Ex: 87654560 is divisible by 5, since the last digit is 0.

5. Divisible by 6: A number is divisible by 6, if following conditions satisfies.

a.       The number should be even.

b.      The sum of all digits should be divisible by 3.

Ex: 35256 is divisible by 6, since it is even and the sum is divisible by 3.

6. Divisible by 8: A number is divisible by 8, if the number formed by the last three digits of the number is divisible by 8.

Ex: 953360 is divisible by 8, since last three digits (360) is divisible by 8.

7. Divisible by 9: A number is divisible by 9, if the sum of the digits is equal to 9.

Ex: 99999 is divisible by 9, since the sum of digits is equal to 9.

8. Divisible by 10: A number is divisible by 10, if its unit digit is 0.

Ex: 123450 is divisible by 10, since its unit digit is 0.

9. Divisible by 11: A number is divisible by 11, If the difference of the sum of its digits at odd places and the sum of even places, is either 0 or a number divisible by 11.

Ex: 999999 is divisible by 11, since the difference of the sum of its digits at odd places and the sum of even places is 0.

10. Divisible by 12: A number is divisible by 12, If it divisible by both 3 and 4.