The Divisibility Rules Calculator is a tool that helps determine whether a number can be evenly divided by another number without performing long division. It applies divisibility rules for common numbers such as 2, 3, 4, 5, and so on. This calculator simplifies calculations for students, teachers, and professionals who need quick divisibility checks.
Formula of Divisibility Rules Calculator
Divisibility Rules:
- Divisibility by 2: A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
- Divisibility by 3: A number is divisible by 3 if the sum of all its digits is divisible by 3.
- Divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
- Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
- Divisibility by 7:
- Method 1: Split the number into groups of three digits from right to left. Find the alternating sum of these groups. If the result is divisible by 7, then the original number is divisible by 7.
- Method 2: Take the last digit, double it, and subtract from the rest of the number. Repeat until you get a recognizable number. If that number is divisible by 7, the original number is divisible by 7.
- Divisibility by 8: A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
- Divisibility by 9: A number is divisible by 9 if the sum of all its digits is divisible by 9.
- Divisibility by 10: A number is divisible by 10 if its last digit is 0.
- Divisibility by 11: A number is divisible by 11 if the alternating sum of its digits (first – second + third – fourth + …) is divisible by 11.
- Divisibility by 12: A number is divisible by 12 if it is divisible by both 3 and 4.
- Divisibility by 13: Take the last digit, multiply by 4, and add to the rest of the number. Repeat until you get a recognizable number. If that number is divisible by 13, the original number is divisible by 13.
- Divisibility by 16: A number is divisible by 16 if the number formed by its last four digits is divisible by 16.
- Divisibility by 25: A number is divisible by 25 if the number formed by its last two digits is 00, 25, 50, or 75.
Quick Reference Table
| Number | Divisibility Rule |
|---|---|
| 2 | Last digit is even (0, 2, 4, 6, 8) |
| 3 | Sum of digits is divisible by 3 |
| 4 | Last two digits form a number divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 7 | Double the last digit, subtract from the rest, repeat until recognizable |
| 8 | Last three digits form a number divisible by 8 |
| 9 | Sum of digits is divisible by 9 |
| 10 | Last digit is 0 |
| 11 | Alternating sum of digits is divisible by 11 |
| 12 | Divisible by both 3 and 4 |
| 13 | Multiply last digit by 4, add to rest, repeat |
| 16 | Last four digits form a number divisible by 16 |
| 25 | Last two digits are 00, 25, 50, or 75 |
Example of Divisibility Rules Calculator
Let’s check if 4,536 is divisible by 9:
- Sum of digits: 4 + 5 + 3 + 6 = 18
- Since 18 is divisible by 9, 4,536 is divisible by 9.
Most Common FAQs
Divisibility rules help perform quick mental math checks without using a calculator. They save time in arithmetic, algebra, and number theory applications.
Yes, they work for any whole number, but they may not apply to decimals or fractions in the same way.
The divisibility rules for 2, 5, and 10 are the easiest because they depend only on the last digit of the number.