About a natural number b we say that it is divisor of a natural number a if there is a natural number c such that a = b • c.
We can say about a that this is a multiple of b.
We write b|a and we read b divide a or b is a divisor of a.
A natural number is divisible by 2 if the last digit is a even figure (0,2,4,6,8).
E.g.: 16 is divisible by 2 (it has the last digit divisible by 2).
37 is not divisible by 2 (because 7, the last digit, is not divisible by 2).
A natural number is divisible by 3 if the sum of its digits are divisible by 3.
E.g.: 32139 is divisible by 3; 3+2+1+3+9=18
A natural number is divisible by 9 if the sum of its digits are divisible by 9. This criterion is similar with 3 Criterion.
E.g.. 21543057 is divisible by 9 9; 2+1+5+4+3+0+5+7=27
A natural number is divisible by 4 if the 2 digits number from the last 2 digits is divisible by 4.
E.g.. 4 | 2032 becouse 4 | 32
4 | 128 becouse 4 | 28.
A natural number is divisible by 5 if the last digit is 0 or 5.
E.g.: 5 | 35, 5 | 110
A natural number is dicisible by 25 if the number from the last 2 digits is divisible by 25.
E.g. 25 | 3850 because 25 | 50
A natural number is divisible by 11 if the difference between the figures located on odd places and sum of the digits located on even places is a multiple of 11.
E.g.: 1925 : 11=175; (9+5)-(1+2)=11
1012 : 11=92; (1+1)-(0+2)=0
A natural number is divisible by 10 if its last digit is 0,
by 100 if its last two digits are 00,
by 1000 if its last 3 digits are 000,
by 10.000 if its last four digits are 0000,
by 100.000 if its last five digits are 00000,
by 1.000.000 if its last six digits are 000000
and so on!
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