In Divisibility Rules (Part-1), we saw rules for divisibility from 2 to 10. Here in Part-2 we will see some more attributions for divisibility:
Divisibility By 11
If the difference of the sums of the alternate digits is divisible by 11, then the original number is also divisible by 11.
1. Starting from the right (one’s) add the digits in the odd positions and the even position.
2. Subtract the smaller number from the larger.
If the difference is '0' or evenly divisible by 11, the original number is divisible by 11 as well.
For example, take the number 181,907.
The numbers 7,9, and 8 are in the odd positions. They sum to 24. The numbers 0,1, and 1 are in the even positions. They sum to 2.
Subtract 2 from 24 to get 22.
22 divides by 11 into 2. So, 181907 is evenly divisible by 11.
Take another number. 16623585 is divisible by 11 since (5+5+2+6)–(8+3+6+1)= 0.
Divisibility by 12
A number is divisible by 12 if it is divisible by both 3 and 4. Use the methods for Divisibility by 3 and Divisibility by 4. If they both work, your number is also evenly divisible by 12.
For example: 34,164 is divisible by 12 because it is divisible by 3 and 4.
For example: 34,164 is divisible by 12 because it is divisible by 3 and 4.
Divisibility by 13
Subtract nine times the last digit from the remaining number. If what is left is divisible by 13, then so is the original number.
Let’s check for divisibility of the number 5,616 by 13.
Nine times the last digit (6) is 54. Now subtract 54 from the remaining number: 561 − 54 = 507. Since we still cannot visually inspect the resulting number for divisibility by 13, we continue the process.
Continue with the resulting number 507, subtract nine times the last digit (9×7) from the remaining number: 50−63=−13, which is divisible by 13; therefore, the original number is divisible by 13.
Another method
Instead of subtracting nine fold the last digit from the remaining number (which works); you could also add the last digit fourfold to the remaining number.
Example: Is 1313 divisible by 13?
131 + 4×3 = 143
14 + 4×3 = 26
2 + 4×6 = 26
Since 26 is divisible by 13, so is 1313.
Divisibility by 14
Check if the last digit of the original number is odd or even. If the number is odd, then the number is not divisible by fourteen. If the number is even, then apply the divisibility rule for 7.
Keep in mind, the odd and even test is to see if the number is divisible by 2. If the original even number is divisible by 7, then it is also divisible by 14. If the original even number is not divisible by 7, it is not divisible by 14.
Divisibility by 15
A number is divisible by 15 if the last digit is 5 and if the sum of all the digits is divisible by 3.
Use the methods for divisibility by 3 and 5. If they both work, the number is also evenly divisible by 15.
Divisibility by 17
Subtract five times the last digit each time from the remaining number until you reach a number small enough to determine its divisibility by 17.
We justify the rule for divisibility by 17 as we did the rules for 7 and 13. Each step of the procedure subtracts a “bunch of 17s” from the original number until we reduce the number to a manageable size and can make a visual inspection of divisibility by 17.
Divisibility by 18
A number is divisible by 18 if it is even and divisible by 9.
Example: Take 108,273,276. The number is even and the digits sum to 36 which divides evenly into 4 by 9, so the number is evenly divisible by 18.
As with the tests for 3, 6 and 9, you can keep adding numbers until you're left with only one digit.
Divisibility by 24
If the number can be evenly divided by 3 and 8, the same can also be said for 24. Use the methods for divisibility by 3 and 8. If they both work, the number is also evenly divisible by 24.
Divisibility by 25
Last two digits must end in 00, 25, 50, or 75. Simple enough!
Divisibility by 33
If the number can evenly be divided by 3 and 11, the same can also be said for 33. Use the methods for Division by 3 and Division by 11 above. If they both work, your number is also evenly divisible by 33.
Dividing by 36
If the number can be evenly divided by 4 and 9, the same can also be said for 36. Use the methods for Division by 4 and Division by 9 above. If they both work, your number is also evenly divisible by 36.
Divisibility by 50
If the number’s last two digits end in 00 or 50, the whole number is divisible by 50.
0 comments