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Divisibility criteria

The divisibility criteria will help us quickly to know if a number is divisible by some other number, for that we will cover the divisibility criteria of each of the number endings and we will also include examples of the divisibility criteria, also known as divisors of a number.

Criteria for divisibility of 2

A number is divisible by 2 if it ends in zero or an even number

  • 836 is divisible by 2 because it ends in an even number
  • 640 is divisible by 2 because it ends in zero
  • 383 is not a number divisible by 2 because it ends in 3.

Criteria for divisibility of 3

A number is divisible by 3 if the sum of its digits is equal to 3 or said sum is easily divisible by 3 or said sum is a multiple of 3.

  • 81 is divisible by 3 because the sum of its digits is 9 and consecutively 9 is a multiple of 3
  • 464922 is divisible by 3 because the sum of its digits is 27 and also if we sum 2+7 it is equal to 9 and 9 is a multiple of 3
  • 73 is not a multiple of 3 because the sum of its digits is 10.

Criteria for divisibility of 4

A number is divisible by 4 if its last two digits are zeros or some multiple of 4.

  • 300 is divisible by 4 because its last two digits are zeros
  • 424 is divisible by 4 because its last two digits are a multiple of 4.

Criteria for divisibility of 5

A number is divisible by 5 if its last digit is 5 or zero.

  • 4865 is divisible by 5 because its last digit is five
  • 690 is divisible by 5 because its last digit is zero.

Criteria for divisibility of 6

A number is divisible by 6 if it is divisible between 2 and 3. It is to consult the divisibility criteria of 2 and 3.

  • 582 is divisible by 6 because it is divisible by 2; and also the sum of its figures is 15, a number divisible by 3.

Criteria for divisibility of 7

This criteria is a bit more complex. A number is divisible by 7 if when doubling the last digit, we subtract it from the rest of the digits and if the result of the subtraction is zero or a multiple of 7, then the number is divisible by 7

  • 4641 is divisible by 7, let’s see the procedure. We double the last digit (1) and subtract it from the rest of the digits: 464 - 2 = 462. It is still difficult to see if it is divisible by 7, so we do the same again, double the last digit and subtract it: 46-4=42. And 42 is an easily identifiable multiple of 7. So 4641 is divisible by 7.

Criteria for divisibility of 8

This criteria is the only one that you will have to do divisions to know if a number is divisible by 8 or not. In some cases it can be beneficial if you have a long number, but in some cases it is better to carry out the division of the whole number when there are not many digits.

The criteria is as follows: a number is divisible by 8 when its last 3 digits are divisible by 8

  • 83656 is divisible by 8 since the number 656 is divisible by 8

It is to do the classic division of the divider box.

Criteria for divisibility of 9

A number is divisible by 9 if the sum of its digits is equal to 9 or a multiple of 9

  • 585 is divisible by 9 because the sum of its digits is 9. 5+8+5=18\rightarrow 1+8 = 9. If the number we sum we know is a multiple of 9, we can save ourselves that step of sum again.
  • 3978 is divisible by 9 because the sum of its digits is 27 and 27 is a multiple of 9. We can still sum those digits 2+7=9.

Criteria for divisibility of 10

A number is divisible by 10 if its last digit ends in zero

  • 2370 is divisible by 10 because its last digit is zero

You are now a master of divisibility criteria.

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