# Divisibility criteria

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

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Divisibility by 2
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**
A number is divisible by 2, if its

**is 0 or is divisible by 2. Numbers, which are divisible by 2 are called**

*last digit**even*numbers. Otherwise, numbers are called

*odd*numbers.

**
Divisibility by 4
.
**
A number is divisible by 4, if its

**are zeros or they make a two-digit number, which is divisible by 4.**

*two last digits*
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Divisibility by 8
.
**
A number is divisible by 8, if its

**are zeros or they make a three-digit number, which is divisible by 8.**

*three last digits*
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Divisibility by 3 and by 9
.
**
A number is divisible by 3, if

**is divisible by 3. A number is divisible by 9, if**

*a sum of its digits***is divisible by 9.**

*a sum of its digits*
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Divisibility by 6
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**
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

**is 0 or 5.**

*last digit*
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Divisibility by 25
.
**
A number is divisible by 25, if its

**are zeros or they make a number, which is divisible by 25.**

*two last digits*
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Divisibility by 10
.
**
A number is divisible by 10, if its

**is 0.**

*last digit*
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Divisibility by 100
.
**
A number is divisible by 100, if its

**are zeros.**

*two last digits*
**
Divisibility by 1000
.
**
A number is divisible by 1000, if its

**are zeros.**

*three last digits*
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Divisibility by 11
.
**
A number is divisible by 11 if and only if a sum of its digits, located on

**is equal to a sum of its digits, located on**

*even places***, OR these sums are differed by a number, which is divisible by 11.**

*odd places*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 ! |