Easy Math Tricks for Elementary School: Is a Number Divisible by ...?

Math seems hard to learn for many kids. Here are some fun and easy math tricks to find out what a whole number is divisible by.

Easy Math Trick #1: Is a Number Divisible by 1?

Yes it is. Any whole number divided by 1 is itself.

Easy Math Trick #2: Is a Number Divisible by 2?

If the last digit is 2, 4, 6, 8 or 0 the number is divisible by 2. For example, the last digit of the number 28,641 is 1, so the number isn't divisible by 2.

Easy Math Trick #3: Is a Number Divisible by 3?

Add the digits together. If the sum of digits is divisible by 3, the original number is too. Not sure if the sum of digits is divisible by 3? Add up the sum's digits and check if the new sum is divisible by 3. You can keep doing this until either you know the answer, or you end up with a single digit sum. If that sum is 3, 6, or 9, the original number is divisible by 3.

For example, is the number 57,973 divisible by 3? Sum up the digits: 5+7+9+7+3=31. Since 31 is not divisible by 3, neither is 57,973. Not sure? Sum up the two digits of the sum 3+1=4, which isn't divisible by 3.

Taking another example, is the number 185,204,859 divisible by 3? Without a calculator it seems impossible to say. But just sum up the digits: 1+8+5+2+0+4+8+5+9=42. If you don't know if 42 is divisible by 3, sum up its digits 4+2=6, which is divisible by 3, so 185,204,859 is too.

Easy Math Trick #4: Is a Number Divisible by 4?

This is a bit trickier, but still easy. First, if the last digit is 1, 3, 5, 7, or 9 the answer is no. To be divisible by 4 a number must be divisible by 2. If your number is divisible by 2, proceed.

For any number, if you can break it down to a sum of other numbers, all of which are divisible by 4, the original number is divisible by 4 as well. The easy math trick here is in choosing the easiest breakdown.

Start out by breaking out any digits from the hundreds up. For example, if your number is 345,276 break that into 300,000+40,000+5,000+200+76. Since 100 is divisible by 4 (100/4=25, just as a dollar is equal to 4 quarters), any number of hundreds is divisible by 4. The same is true for thousands, tens of thousands, etc.

Now the problem has been simplified to the 2-digit number formed by the tens digit and the units, 76 in our example. If 76 is divisible by 4, so is 345,276. Break down 76 into 20+20+20+16. Since 20 is divisible by 4 (20/4=5, just as 20 cents are equal to 4 nickels), our problem has been simplified further, to: is 16 divisible by 4?

To check this out, divide by 2, getting 8. Since 8 is even, it can be divided by 2 again, meaning that 16 is divisible by 2 twice, meaning it's divisible by 4. Thus 76 is divisible by 4, and so is 345,276.

To summarize, the easy math trick here is to ignore any digits from the hundreds on up, subtract 20 from the remaining 2-digit number as many times as you can without going below zero, then try to divide the remaining number by 2 twice. If you succeed, the original number is divisible by 4.

Easy Math Trick #5: Is a Number Divisible by 5?

This one is easier than most of the above. If the last digit is 0 or 5, the number is divisible by 5. For example, the last digit of the number 14,275 is 5, so the number is divisible by 5.

Easy Math Trick #6: Is a Number Divisible by 6?

The easy math trick here is that a number is divisible by 6 if and only if it is divisible by both 2 and 3. Use the above easy math tricks to find out if your number is divisible by 2 and 3. If the answer is yes to both, it is divisible by 6. If the answer to one and/or the other is no, it is not divisible by 6.

For example, the number 45,379 ends in a 9 so it isn't divisible by 2, and thus not divisible by 6. The number 45,378 on the other hand is divisible by 2. If you sum up its digits: 4+5+3+7+8=27, the sum is divisible by 3 (if not sure, sum up those two digits 2+7=9 and you'll see). Thus 45,378 is divisible by 6.

Easy Math Trick #7: Is a Number Divisible by 9?

Just as with easy math trick #3 above, sum up the digits of any number. If the sum of digits is divisible by 9, so is the original number. For example, is the number 1,946,961,045 divisible by 9? The sum of its digits, 1+9+4+6+9+6+1+0+4+5=45 is divisible by 9, so the answer is yes. If you're not sure, sum up again the digits of the sum 4+5=9, which is divisible by 9.

Easy Math Trick #8: Is a Number Divisible by 10?

If the last digit of your number is 0, the answer is yes. Otherwise it isn't.

Easy Math Trick #9: Is a Number Divisible by 12?

Similar to divisibility by 6, divisibility by 12 depends on the answers to two easy math tricks above. Here, since 12=3x4, a number is divisible by 12 if and only if it's divisible by both 3 and 4 so use easy math tricks #3 and #4 above.

Easy Math Trick #10: Is a Number Divisible by 15?

Another composite math trick helps here. Since 15=3x5, use easy math tricks #3 and #5 above. If your number is divisible by both 3 and 5 it is divisible by 15.

Easy Math Trick #11: Is a Number Divisible by 20?

Similar to easy math trick #4, we can break any number down to a sum of simpler numbers. The hundreds, thousands, etc. are all divisible by 20. The question remains then only about the remaining 2-digit number. If your number's last 2 digits are 20, 40, 60, 80, or 00 your original number is divisible by 20. Otherwise it isn't.

The above 11 easy math tricks let you find out without a calculator if a number is divisible by 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, and/or 20. Other math tricks let you see if a number is divisible by other numbers, but not quite as easily. Usually it requires division calculations and/or use of 3 or more of the above easy math tricks together.