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Divisibility criteria


Divisibility of numbers by 2, 4, 8, 3, 9, 6, 5, 25, 10, 100, 1000, 11.

Divisibility by 2. A number is divisible by 2, if its last digit is 0 or is divisible by 2. Numbers, which are divisible by 2 are called even numbers. Otherwise, numbers are called odd numbers.

Divisibility by 4. A number is divisible by 4, if its two last digits are zeros or they make a two-digit number, which is divisible by 4.

Divisibility by 8. A number is divisible by 8, if its three last digits are zeros or they make a three-digit number, which is divisible by 8.

Divisibility by 3 and by 9 . A number is divisible by 3, if  a sum of its digits is divisible by 3. A number is divisible by 9, if a sum of its digits is divisible by 9.

Divisibility by 6. A number is divisible by 6, if it is divisible by 2 and by 3.

Divisibility by 5. A number is divisible by 5, if its last digit is 0 or 5.

Divisibility by 25. A number is divisible by 25, if its  two last digits are zeros or they make a number, which is divisible by 25.

Divisibility by 10. A number is divisible by 10, if its last digit is 0.

Divisibility by 100. A number is divisible by 100, if its two last digits are zeros.

Divisibility by 1000. A number is divisible by 1000, if its three last digits are zeros.

Divisibility by 11. A number is divisible by 11 if and only if a sum of its digits, located on even places is equal to a sum of its digits, located on odd places,  OR  these sums are differed by a number, which is divisible by 11.

There are criteria of divisibility for some other numbers, but these criteria are more difficult and not considered in a secondary school program.

E x a m p l e . A number 378015 is divisible by 3, because a sum of its digits 3 + 7 + 8 + 0 + 1 + 5 = 24, which is divisible by 3. This number is divisible by 5, because its last digit is 5. At last, this number is divisible by 11, because a sum of even digits: 7 + 0 + 5 =12 and a sum of odd digits: 3 + 8 + 1 = 12 are equal. But this number isnít divisible by  2, 4, 6, 8, 9, 10, 25, 100 and 1000, because Ö Check these cases yourself !

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