The given number is divisible by:
2 : If the units place contains 0 or any even number.
Ex: 120,342,894,766,328 are divisible by 2.
3 : If the sum of all digits is divisible by 3.
Ex: 123(1+2+3=6).since 6 is divisible by 3,123 is also divisible by 3.
329(3+2+9=14)since 14 is not divisible by 3,329 is also not divisible by 3.
9012(9+0+1+2=12)since 12 is divisible by 3,9012 is also divisible by 3.
4 : If the last 2 digits are 0's or multiple of 4,then the entire number is divisible by 4.
Ex: 9100(is divisible by 4 since there are two 0's at the end)
8732(32 is divisible by 4.hence 8732 is also divisible by 4)
324(24 is divisible by 4.hence 324 is also divisible by 4)
5 : If last digit is either 0 or 5.
Ex: 230,905,1785 are divisible by 5.
6 : If the given number is divisible by both 2 and 3.
Ex: 852,474,946 are divisible by both 2 and 3.Hence divisible by 6.
7 : If the difference between double of units digit and the remaining number is divisible by 7.If the number is large enough,process is repeated.
Ex: 161[16-(2*1)=14.Since 14 is divisible by 7,161 is also divisible by 7.
1561[156-(2*1)=154.15-(2*4)=7.Since 7 is divisible by 7,1561 is also divisible by 7]
8 : If last 3 digits are either 0's or multiple of 8,then the entire number is divisible by 8.
Ex: 639000(is divisible by 8 since there are 3 0's at the end)
968456(is also divisible by 8 since 456 is divisible by 8)
9 : If the sum of digits is exactly divisible by 9 then th number is also divisible by 9.
Ex: 2529(2+5+2+9=18.since 18 is divisible by 9,2592 is also divisible)
10: If there is a zero in the units place.
Ex; 120,8760,7610 are divisible by 10.
11: If the difference between sum of digits at even place and odd place is either 0 or divisible by 11,then the number is divisible by 11.
Ex: In 132,[(1+2=3),3-3=0]hence divisible by 11.
12: If the number is divisible by both 3 and 4,then it is divisible by 12.
14: If the number is divisible by both 2 and 7,then it is divisible by 14.
15: If the number is divisible by 3 and 5,then the number is divisible by 15.
18: If the number is divisible by 9 and 2 then the number is divisible by 18.
25:If the last 2 digits are 0's or they are divisible by 25,then the entire number is divisible by 25.
99: Starting from right,make the pairs of 2 digits and add all the pairs.If the sum is divisible by 99,then the number is divisible by 99.
Ex: In 297(97+2=99)hence divisible by 99.
In 676269(69+62+67=198)since 198 is a multiple of 99,676269 is also divisible by 99.
999:Starting from right,make pairs of 3 digits each and add all the pairs and if the sum is multiple of 999,then the number is divisible by 999.
Rules of divisibility test(made easy)