Table of Contents
Divisibility Rules from 1 t0 20
Divisibility rules are methods that tell whether a number can be exactly divided by another number or not. we divide this topic in many parts, to make easy and under stable. we divide this in four parts as follows:
Divisibility Rules for 1,2,3,4,5,6,7,8,9,10
Divisibility Rules for even numbers from 1 to 010
Law of divisibility by 2: Every even number is divisible by 2. In other words, a number whose unit digit is 0, 2, 4, 6 or 8 is divisible by 2.
Like: 154, 6516, 827720, 1000
Law of divisibility by 4: Any number made up of units and tens digits is divisible by 4.
Like: 772724, 7266260, 722612
The number whose units and tens digits are zero is also divisible by 4.
Like: 6161600, 72616000
Law of divisibility by 6: A number which is divisible by both 2 and 3 is also divisible by 6.
Like: 65252, 98016
Law of divisibility by 8: Numbers made up of units, tens and hundreds digits are divisible by 8.
Like: 176888, 107568
In the number whose units, tens and hundreds digits are zero, 8 is also subtracted.
Like: 626000, 81717000
Law of divisibility by 10: The number whose unit digit is zero is divisible by 10.
Like: 16160, 76640
Divisibility Rules for ODD numbers from 1 to 010
Law of divisibility by 3: The number whose sum of all its digits is divisible by 3 is divisible by 3.
For example: 65175 => 6+5+1+7+5=24
The sum of the digits is 24 and 24 is divisible by 3, hence 65175 is divisible by 3.
Rule of divisibility by 5: The number whose unit digit is 0 or 5 is divisible by 5.
Like: 626260, 71625
Law of divisibility by 7: If the number obtained by subtracting double the digit of a given number from the remaining number (except the ones digit) is divisible by 7, then the entire number will be divisible by 7.
For example: The units digit in 343 is 3.
By subtracting double of 3 from the remaining number
(34 – 6 = 28)
The two-digit number 28 is divisible by 7, so 343 is also divisible by 7.
Note: If after subtracting you still get a larger number, keep repeating these steps.
If the unit digit of a given number is multiplied by 5 and added to the remaining number, if the number obtained is divisible by 7, then the entire number will also be divisible by 7.
Like- 273
- Step 1: Multiply the ones digit by 5
(3×5=15) - Step 2: Add the product to the remaining numbers except the ones digit.
(15 + 27 = 42)
42 is divisible by 7 so 273 is also divisible by 7
If after adding the product and the remaining numbers, a larger number still remains, repeat these - steps:-
Number: 9548 - Step 1: (8 × 5 = 40)
- Step 2: (40 + 954 = 994)
Repeat both the steps again taking the number 994, - Step 3: (4 × 5 = 20)
- Step 4: (20 + 99 = 119)
Repeat both the steps again taking number 119, - Step 5: (9 × 5 = 45)
- Step 6: (45 + 11 = 56)
The two-digit number 56 is divisible by seven, so 9548 is also divisible by 7.
Law of divisibility by 9: The number whose sum of digits is divisible by 9 is divisible by 9.
Example: 71667 (sum of digits 27), 926595 (sum of digits 36)
Divisibility Rules from 11 to 20
https://www.youtube.com/watch?v=QqSH8npBY2Q
Divisibility Rules from 11 to 20
Law of divisibility by 11: The number whose sum of digits in even places and odd places is equal is divisible by 11.
Like: 3267, 52173, 89012
In 52173,
- Sum of digits at even places = 2 + 7 = 9
- Sum of digits at odd places = 5 + 1 + 3 = 9
- Hence 52173 is divisible by 11.
Law of divisibility by 12: A number that is divisible by both 3 and 4 is also divisible by 12.
Like: 4632, 50712
Law of divisibility by 13: If four times the unit digit of a number is added to the number made up of the remaining digits, the resulting sum is divisible by 13, then that number will also be divisible by 13.
Like: 2639, 5499
Law of divisibility by 14: A number that is divisible by both 2 and 7 is also divisible by 14.
Like: 266, 672, 1554
Law of divisibility by 15: A number that is divisible by both 3 and 5 is also divisible by 15.
Like: 9765, 15690
Law of divisibility by 16: The number whose last four digits are divisible by 16 is divisible by 16.
If the number has an even digit in the thousands place and the number made up of the last three digits is divisible by 16, then the entire number is divisible by 16.
The number which has an odd digit in the thousand place is also divisible by 16 and if 8 is added to the number made up of the last three digits, then it becomes divisible by 16.
Like: 512, 944, 1424
Law of divisibility by 17: If a number is divisible by 17 then when 5 times the unit digit is subtracted from the number formed by the remaining digits then the whole number will be divisible by 17.
Like: 2074, 391
Repeat both these steps again and again if the number is high.
Law of divisibility by 18: A number that is divisible by both 3 and 6 is also divisible by 18.
Like: 702, 2286
Law of divisibility by 19: If twice the unit digit of a number is added to the number made up of the remaining digits, the resulting number becomes divisible by 19, then the whole number becomes divisible by 19.
Like: 703, 1881, 2299
If the numbers are large, repeat these two steps again and again.
Law of divisibility by 20: A number that is divisible by both 4 and 5 is also divisible by 20.
Like: 2900, 1582