Operations on Numbers

Operations on Numbers

Divisibility Rules:

A number is divisible by 2 if it is an even number.

A number is divisible by 3 if the sum of the digits is divisible by 3.

A number is divisible by 4 if the number formed by the last two digits is divisible by 4. A number is divisible by 5 if the units digit is either 5 or 0.

A number is divisible by 6 if the number is also divisible by both 2 and 3.

A number is divisible by 8 if the number formed by the last three digits is divisible by 8.

A number is divisible by 9 if the sum of the digits is divisible by 9.

A number is divisible by 10 if the units digit is 0.

A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places, is divisible by 11.

A number is divisible by 12 if the number is also divisible by both 3 and 4.

POINT TO REMEMBER FOR SPECIAL CASE –

For Divisibility of 7 – We take Unit digit & multiply with 2 then Substract . For Divisibility of 13 – We take Unit digit & multiply with 4 then Add .

For Divisibility of 17 – We take Unit digit & multiply with 5 then Substract .

For Divisibility of 19 – We take Unit digit & multiply with 2 then Add .

# A number is divisible by 7 if it Follows the below rules:

First of all we recall the osculator for 7. Once again , for your convenience , as 7×3 = 21 (One More than 2 X 10), our negative osculator is 2 . This Osculator ‘2’ is our key – digit . This and only this digit is used to check the divisibility of any number by 7.

See how it works –

Ex. Is 112 divisible by 7 ?

Step I : 112 : 11 – 2×2 = 7 (Separate the last digit & multiply with two & then subtract)

Here we can see 7 Is divisible by 7, then we can say 112 is also divisible by 7.

Ex. Is 2961 divisible by 7?

Step I : 296 – 1X2 = 294

Step II : 29 – 4X2 = 21 .

Here we can see 21 Is divisible by 7, then we can say 2961 is also divisible by 7 .

Note : Same Process will be applicable for Bigger Number .

# A number is divisible by 13 if it Follows the below rules: Ex. Is 143 divisible by 13 ?

Step I : 14 + 3X4 = 26 .
Here we can see 26 Is divisible by 13, then we can say 143 is also divisible by 13 .

# A number is divisible by 17 if it Follows the below rules Ex. Is 1904 divisible by 17 ?

Step I : 190 – 4X5 = 170 .

Here we can see 170 Is divisible by 17 . then we can say 1904 is also divisible by 17 .

# A number is divisible by 19 if it Follows the below rules Ex. Is 149264 divisible by 19 ?

Step I : 14926 + 4X2 = 14934 .

Step II : 1493 + 4X2 = 1501

Step III : 150 + 1X2 = 152 Step IV : 15 + 2X2 = 19

Here we can see 19 Is divisible by 19 . then we can say 149264 is also divisible by 19 .