Divisibility
A number, b, is divisible by another number, a, if the division is exact.
Rules of Divisibility
Divisible by 2
A number is divisible by 2, if its last digit is a zero or an even number.
24, 238, 1,024.
Divisible by 3
A number is divisible by 3, if the sum of its digits is a multiple of 3.
564
5 + 6 + 4 = 15, is multiple 3
2,040
2 + 0 + 4 + 0 = 6, is multiple 3
Divisible by 5
A number is divisible by 5, if it ends in zero or five.
45, 515, 7,525.
Divisible by 7
A number is divisible by 7, when the difference between the number without the figure of the units and the double the number of the units is 0 or a multiple of 7.
343
34 − 2 · 3 = 28, is multiple of 7.
105
10 − 5 · 2 = 0
2261
226 - 1 · 2 = 224.
Repeat the process with 224.
22 − 4 · 2 = 14, is multiple of 7.
Divisible of 11
A number is divisible by 11, if the difference between the sum of the figures who occupy the even numbers and the odd numbers is 0 or a multiple of 11.
121
(1 + 1) − 2 = 0
4,224
(4 + 2) − (2+4) = 0
Other rules
Divisible by 4
A number is divisible by 4, if the last two digits are zeros or a multiple of 4.
36, 400, 1,028.
Divisible by 6
A number is divisible by 6, if it is divisible by 2 and 3.
72, 324, 1503
Divisible by 8
A number is divisible by 8, if its last three figures are zeros or a multiple of 8.
4000, 1048, 1512.
Divisible by 9
A number is divisible by 9, if the sum of its digits gives a multiple of 9.
81
8 + 1 = 9
3,663
3 + 6 + 6 + 3 = 18, is multiple of 9
Divisible by 10
A number is divisible by 10, if the last figure in the unit is 0.
130, 1,440, 10,230
Divisible by 25
A number is divisible by 25, if their last two digits are zeros or a multiple of 25.
500, 1,025, 1,875.
Divisible by 125
A number is divisible by 125, if its last three figures are zeros or a multiple of 125.
1,000, 1,125, 4,250.
Factoring
Factoring a number into prime factors is to express the number as a product of prime numbers.
