Tests for Even Divisibility
Any number that ends in 0,2,4,6 or 8 is evenly divisible by 2.
Division by 3Add the number's digits. If the sum is evenly divisible by 3, then so is the number. Example: does 3 divide evenly into 2,169,252? Yes it does, because the sum of the digits is 27, and 27 is divisble by 3. If you prefer, you can keep adding numbers until one digit remains. For example, continuing with 27, \(2 + 7 = 9\), which is also evenly divisible by 3.
Division by 4If the number's last 2 digits are 00 or if they form a 2-digit number evenly divisible by 4, then number itself is divisible by 4. How about 56,789,000,000? Last 2 digits are 00, so it's divisible by 4. Try 786,565,544. Last 2 digits, 44, are divisible by 4 so, yes, the whole number is divisible by 4.
Division by 5Any number that ends in a 0 or 5 is evenly divisible by 5.
Division by 6The number has to be even. If it's not, forget it. Otherwise, add up the digits and see if the sum is evenly divisible by 3. It it is, the number is evenly divisible by 6. Try 108,273,288. The digits sum to 39 which divides evenly into 13 by 3, so the number is evenly divisible by 6. If you want, you can keep adding numbers until only one digit remains and do the same thing. So in this case, 3 + 9 = 12 and 1 + 2 = 3, and 3 is evenly divisible by 3.
Division by 7Multiply the last digit by 2. Subtract this answer from the remaining digits. Is this number evenly divisible by 7? If it is, then your original number is evenly divisible by 7. Try 364. 4, the last digit, multiplied by 2 = 8. 36, the remaining digits, minus 8 = 28. 28 is evenly divisble by 7, and thus, so is 364
Division by 8If the number's last 3 digits are 000 or if they form a 3-digit number evenly divisible by 8, then the number itself is divisible by 8. How about 56,789,000,000? Last 3 digits are 000, so it's divisible by 8. Try 786,565,120. The last 3 digits, 120, divide by 8 into 15, so yes, the whole number is divisible by 8.
Division by 9Sum the number's digits. If it divides by 9, it is evenly divisble by 9. As with the tests for 3 and 6, you can keep adding numbers until you're left with only one digit.
Division by 10Any number that ends in 0 is evenly divisible by 10.
Division by 11Here are four methods:
If the number can be evenly divided by 3 and 4, the same can also be said for 12. Use the methods for Division by 3 and Division by 4 above. If they both work, your number is also evenly divisible by 12.
Division by 15If the number can be evenly divided by 3 and 5, the same can also be said for 15. Use the methods for Division by 3 and Division by 5 above. If they both work, your number is also evenly divisible by 15.
Division by 24If the number can be evenly divided by 3 and 8, the same can also be said for 24. Use the methods for Division by 3 and Division by 8 above. If they both work, your number is also evenly divisible by 24.
Division by 33If the number can be evenly 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.
Division by 36If 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.
Back to the home page.