Learn just how to check if a number is divisible through 7, 8, or 9, and also find out why every of these divisibility tests actually work.

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Two weeks earlier we looked at exactly how to quickly test even if it is or not a number is divisible through 2 or 3, and last week us learned a couple of clever tricks the you have the right to use to check whether or no a number is divisible by 4, 5, or 6. For this reason what’s the logical following step for us? Well, now we’re walk to complete up this collection by learning how to check whether or not a number is divisible through 7, 8, or 9.

How come Tell if a Number is Divisible by 7

The quick and also dirty reminder to check a number because that divisibility through 7 is a three actions process:Take the last digit of the number you’re testing and double it.
Subtract this number indigenous the rest of the digits in the initial number.If this new number is one of two people 0 or if it’s a number that’s divisible by 7, then you know that the initial number is likewise divisible by 7. If girlfriend can’t quickly tell yet if the brand-new number is divisible by 7, go earlier to the an initial step v this brand-new smaller number and shot again.
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For example, is the number 203 divisible by 7? Well, let’s use our three step process to uncover out:The last digit of 203 is 3, so double that is 3 x 2 = 6.Subtracting this new number, 6, indigenous 20 (the remaining digits that the initial number 203) provides 14.Since 14 is divisible through 7, we can instantly tell that the initial number, 203, must likewise be divisible through 7.Let’s shot a larger number. Is 2,023 divisible through 7?The critical digit that 2,023 is 3, so double that is 6.Subtracting 6 native 202 (the staying digits from 2,023) offers us 202 – 6 = 196.Is 196 divisible by 7? I’m not sure. For this reason let’s repeat the process using the new number 196. The final digit that 196 is 6, so twice that is 12. Individually this indigenous 19 (the staying digits that 196) leaves us through 19 – 12 = 7. Since 7 definitely is divisible by 7, we automatically know that the initial number, 2,023, is divisible by 7 too!

Why go the Divisibility by 7 test Work?

Okay, that’s easy enough to do, yet it’s absolutely a little strange…how have the right to that in reality work? Well, that’s a an excellent question, yet unfortunately the reasonable behind this cheat is a little bit too complicated for me to explain here. So despite I generally don’t execute this, in this case I’m walking to leaving the explanation of the divisibility by 7 trick for a later on date. In the meantime, if you’re interested in understanding more, girlfriend can inspect out the explanation found in the “Addendum” ar at the bottom the this page.

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About the Author


Jason Marshall, doctor
Jason Marshall is the author of The math Dude's Quick and also Dirty guide to Algebra. He offers clear explanations of mathematics terms and principles, and his an easy tricks for solving an easy algebra problems will have also the most math-phobic person looking front to functioning out everything math problem comes their way.