Are there computations that you can do mentally that cannot be done with a calculator? Yes! God created our minds to do some amazing things. In this blog I’ll show you 6 math tricks that you compute using only your mind.

I’ll provide a written explanation of these math tricks below but I would highly recommend you watch the above video to get the best explanation of these math tricks.

Math Trick 1: Dividing Factorials

A quick review: Four factorial is 4 X 3 X 2 X 1 = 24 ; we write that as 4! if you are looking for it on your calculator, but of course we’re not using calculators for these calculations.

Dividing by Factorials
Math trick to divide factorials

The problem with using a calculator for computing factorials is that the numbers get very large very quickly, often resulting in an error or overflow message. However, if you know the pattern of (n+1)!/n! = (n+1) then you can quickly compute the answer of any large factorial division problem. For example, 2000!/1999! is simply 2000 .

Math Trick 2: Squaring Numbers Ending in 5

Let’s move on to our next trick which is squaring numbers that end in “5” without using a calculator.

Squaring Large Numbers
Math trick to square large numbers

Let’s square 65. To do this, we can multiply 6 X 7 = 42 (this is taking the first digit in “65” which is a “6” and multipling it by 1 + itself which is “7”). After this we can simply multiply the last digit in “65” (the number “5”) by itself ( 5 X 5 = 25 ) and combine it with the “42”. So, the answer is 4225 .

Want another example? Lets try to square 195. To solve this we simply multiply 19 X 20 = 380 , multiply 5 X 5 = 25 and then combine the two answers. The answer to this problem is 38,025 .

Math Trick 3: Multiplying Numbers that Add up to 10

Working off of the same principle mentioned in the previous trick, we can also multiply large numbers whose last digits add up to 10.

Let’s use 83 X 87 as an example.

Multiplying Numbers that add up to 10
Math trick to multiply numbers that add up to 10

Notice that the last digits of this problem (3 + 7) add up to 10 and other digits are both 8 . Because this is case we can simply multiply 8 X 9 =72 and then multiply 3 X 7 = 21 . This means that the answer to the problem is 7221 .

Math Trick 4: Find the Remainder when Dividing by 9

One last trick: Finding the remainder when dividing by 9. Once again, this one is easy to discover by doing a few examples.

Notice that 23 / 9 = 2 remainder 5 ; and 34 / 9 = 3 remainder 7 . In both cases, you see that the remainder is the sum of the digits (2 + 3 = 5 and 3 + 4 = 7) .

Since the remainder will always be a number between 0 and 8, we need some additional rules. If you add up the digits and get 9, the remainder is 0. If you get a number greater than 9, add the digits up again. For example, if the number is 34291 , we add the digits up (3 + 4 + 2 + 9 + 1) and get 19 ; add those digits (1 + 9) and get 10 ; add those digits (1 + 0) and get 1 ; so the remainder when dividing by 9 would be 1.


I hope you enjoyed stretching your mental math capabilities a little bit. Your mind is more amazing than any machine. I’d like to challenge you to try these math tricks at home and let us know in the comment section how they turned out for you.

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