Divisibility criteria
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 isn’t divisible by 2, 4, 6, 8, 9, 10, 25, 100 and 1000, because … Check these cases yourself ! |