MATHMANIA: HOW TO KNOW IF A NUMBER IS DIVISIBLE BY 7

The quick and easy tip to test a number for divisibility by 7 is a three steps process:

1. Take the last digit of the number you’re testing and double it.
2. Subtract this number from the rest of the digits in the original number.
3. If this new number is either 0 or if it’s a number that’s divisible by 7, then you know that the original number is also divisible by 7. If you can’t easily tell yet if the new number is divisible by 7, go back to the first step with this new smaller number and try again.

For example, is the number 203 divisible by 7? Well, let’s use our three step process to find out:

1. The last digit of 203 is 3, so double that is 3 x 2 = 6.
2. Subtracting this new number, 6, from 20 (the remaining digits of the original number 203) gives 14.
3. Since 14 is divisible by 7, we can immediately tell that the original number, 203, must also be divisible by 7.

Let’s try a larger number. Is 2,023 divisible by 7?

1. The last digit of 2,023 is 3, so double that is 6.
2. Subtracting 6 from 202 (the remaining digits from 2,023) gives us 202 – 6 = 196.
3. Is 196 divisible by 7? I’m not sure. So let’s repeat the process using the new number 196. The final digit of 196 is 6, so twice that is 12. Subtracting this from 19 (the remaining digits of 196) leaves us with 19 – 12 = 7. Since 7 certainly is divisible by 7, we immediately know that the original number, 2,023, is divisible by 7 too!

ENJOY!!!! MATH IS LOGIC, MATH IS FUN!!!
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SOURCE: QUICK AND DIRTY TIPS