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Sep02

Divisibility Guidelines for 7 and 13

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In this post, we are going to learn the divisibility guidelines for numbers 7 and 13.

Divisibility Guidelines for 7

In order to know if a number is divisible by 7, we take the number without the units digit and subtract two times the units digit from this number. Then use the resulting number and repeat the process. Repeat until you have 0, or another number that obviously has 7 as a factor. Otherwise, the number is not divisible by 7.

Here is an example:divisibility guidelines

Procedure:

  • First, we separate the Units digit of the number:

divisibility guidelines

  • After we double the units digit and then subtract this result from the number without the units digit (remember to do multiplication before subtraction!):

4×2= 8

827 – 8= 819

As the number continues to get smaller, we repeat the procedure:

  • We separate the units digit of the number above and continue the procedure:

divisibility guidelines

  • We double the units digit and then subtract this result from the number without the units digit:

81 – 2 x 9 =

81 – 18 = 63

If you recognize that 63 is divisible by 7, you can stop here. Otherwise, repeat the procedure.

  • Separate the units digit of the number above:

divisibility guidelines

6 – 2 x 3 =

6 – 6 = 0

We have ended up with 0.  Therefore, 8274 is indeed divisible by 7.

Divisibility Guidelines for 13

In order to know if a number is divisible by 13, we use the same procedure as above except that instead of doubling the units digit, we multiply it by 9.

If this subtraction results in 0 or has a factor of 13, then the number is divisible of 13.

Here is an example:divisibility guidelinesProcedure:

  • Separate the units digit from the number:

divisibility guidelines

  • We multiply the units digit by 9 and then subtract this result from the number without the units digit (remember to do multiplication before subtraction!):

370 – 9 x 5 =

370 – 45 = 325

Repeat the procedure:

  • Separate the units digit from the number:

divisibility guidelines

  • Multiply the units digit by 9 and then subtract this result from the number without the units digit:

32 – 9 x 5 =

32 – 45 =

Note: When the minuend (32) is less than the subtrahend (45), we reverse subtraction:

45 – 32 =13

The answer is 13. As it is a multiple of 13, the number 3705 is also divisible by 13.

If you want to learn more about divisibility criteria, you can read our previous post for divisibility criteria by 3, 4, 9 and 11.

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