Divisibility and factors

A number is considered divisible by another number (divisibility) when the result of the division is an integer and there is no remainder. The number which divides that number is called a factor of that number or its divisor. Division is an operation that is the opposite of multiplying and the property that a number can be divided by another number is called divisibility.
For example: If you divide the number 16 with the number 2, you will get the number 8 as a result and no remainder. That means that the number 16 is divisible by the number 2 and that 2 is a factor of 16. But if you divide the number 16 with the number 3, you will get the number 5 as a result with 1 as the remainder. This means that 16 is not divisible by 3 and 3 is not a factor of 16.

The basic rules that can help you determine whether a number can be divided by another number (and which one) are ilustrated in the picture below. These rules are particularly useful in prime factorization or finding the least common multiple or the greatest common factor.

division

Divisibility exams for teachers

Exam Name File Size Downloads Upload date
Positive integers
Divisibility of positive integers – very easy 107.1 kB 3429 October 13, 2012
Divisibility of positive integers – easy 157.4 kB 2404 October 13, 2012
Divisibility of positive integers – medium 164.8 kB 3097 October 13, 2012
Divisibility of positive integers – hard 179.1 kB 2371 October 13, 2012
Positive decimals
Divisibility of positive decimals – very easy 559.2 kB 1052 October 13, 2012
Divisibility of positive decimals – easy 572.4 kB 1004 October 13, 2012
Divisibility of positive decimals – medium 575.7 kB 996 October 13, 2012
Divisibility of positive decimals – hard 561.3 kB 992 October 13, 2012
Positive fractions
Divisibility of positive fractions – very easy 119 kB 1046 October 13, 2012
Divisibility of positive fractions – easy 564.6 kB 937 October 13, 2012
Divisibility of positive fractions – medium 572.1 kB 990 October 13, 2012
Divisibility of positive fractions – hard 576.9 kB 851 October 13, 2012
Positive mixed numbers
Divisibility of positive mixed numbers – easy 568.8 kB 972 October 13, 2012
Divisibility of positive mixed numbers – medium 583.9 kB 846 October 13, 2012
Divisibility of positive mixed numbers – hard 612.3 kB 862 October 13, 2012
Positive improper fractions
Divisibility of positive improper fractions – very easy 170.5 kB 860 October 13, 2012
Divisibility of positive improper fractions – easy 564.5 kB 832 October 13, 2012
Divisibility of positive improper fractions – medium 564.4 kB 794 October 13, 2012
Divisibility of positive improper fractions – hard 574.6 kB 849 October 13, 2012
Divisibility of positive improper fractions – very hard 574.1 kB 802 October 13, 2012
Non positive integers
Divisibility of integers – very easy 82.3 kB 944 October 13, 2012
Divisibility of integers – easy 154.6 kB 1024 October 13, 2012
Divisibility of integers – medium 163.2 kB 1235 October 13, 2012
Divisibility of integers – hard 173.4 kB 1287 October 13, 2012
Non positive decimals
Divisibility of decimals – very easy 567.8 kB 901 October 13, 2012
Divisibility of decimals – easy 559.9 kB 963 October 13, 2012
Divisibility of decimals – medium 557 kB 867 October 13, 2012
Divisibility of decimals – hard 559.6 kB 1092 October 13, 2012
Non positive fractions
Divisibility of fractions – very easy 552.2 kB 893 October 13, 2012
Divisibility of fractions – easy 569.2 kB 888 October 13, 2012
Divisibility of fractions – medium 571.5 kB 841 October 13, 2012
Divisibility of fractions – hard 595.4 kB 880 October 13, 2012
Non positive mixed numbers
Divisibility of mixed numbers – easy 559.7 kB 856 October 13, 2012
Divisibility of mixed numbers – medium 588.7 kB 849 October 13, 2012
Divisibility of mixed numbers – hard 585.2 kB 800 October 13, 2012
Non positive improper fractions
Divisibility of improper fractions – easy 175 kB 1028 October 13, 2012
Divisibility of improper fractions – medium 183.4 kB 935 October 13, 2012
Divisibility of improper fractions – hard 212.8 kB 1156 October 13, 2012

 

There are tricks and shortcuts in the process of determination whether a number is divisible by another number.
Every number, including prime numbers, is divisible by the number 1 and itself.
All even numbers (those ending in 0, 2, 4, 6 or 8 ) are divisible by 2.
If you calculate the sum of all the digits in a number and that sum is divisible by 3, then the number is divisible by 3 as well.
A number is divisible by 4 if the last two digits in that number are divisible by 4.
Every number ending in 0 or 5 is divisible by the number 5.
A number is divisible by 6 if it is also divisible by 2 and 3.
If the last three digits in a number are divisible by 8, then that whole number is divisible by 8.
The same rule applies for checking if a number is divisible by the number 9 as it does for number 3. If the sum of all digits in the number is divisible by 9, then the entire number is divisible by 9.
Every number ending in 0 is divisible by the number 10.

Factoring exams for teachers

Exam Name File Size Downloads Upload date
Factoring all positive factors 119.1 kB 2005 October 13, 2012
Factoring numbers without exponents 125.7 kB 1243 October 13, 2012
Factoring with exponents 129.8 kB 1489 October 13, 2012


Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 137.7 kB 1581 October 14, 2012
Divisibility of positive decimals 192.9 kB 999 October 14, 2012
Divisibility of positive fractions 252.6 kB 860 October 14, 2012
Divisibility of positive mixed numbers 227 kB 830 October 14, 2012
Divisibility of positive improper fractions 248.8 kB 861 October 14, 2012
Non positive
Divisibility of integers 143.7 kB 1021 October 14, 2012
Divisibility of decimals 222.3 kB 897 October 14, 2012
Divisibility of fractions 260.9 kB 953 October 14, 2012
Divisibility of mixed numbers 276.9 kB 843 October 14, 2012
Divisibility of improper fractions 234.4 kB 873 October 14, 2012
Factoring numbers
Factoring 198.2 kB 1583 October 14, 2012


Divisibility knowledge test