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 3259 October 13, 2012
Divisibility of positive integers – easy 157.4 kB 2307 October 13, 2012
Divisibility of positive integers – medium 164.8 kB 2950 October 13, 2012
Divisibility of positive integers – hard 179.1 kB 2237 October 13, 2012
Positive decimals
Divisibility of positive decimals – very easy 559.2 kB 967 October 13, 2012
Divisibility of positive decimals – easy 572.4 kB 943 October 13, 2012
Divisibility of positive decimals – medium 575.7 kB 940 October 13, 2012
Divisibility of positive decimals – hard 561.3 kB 930 October 13, 2012
Positive fractions
Divisibility of positive fractions – very easy 119 kB 970 October 13, 2012
Divisibility of positive fractions – easy 564.6 kB 857 October 13, 2012
Divisibility of positive fractions – medium 572.1 kB 907 October 13, 2012
Divisibility of positive fractions – hard 576.9 kB 790 October 13, 2012
Positive mixed numbers
Divisibility of positive mixed numbers – easy 568.8 kB 903 October 13, 2012
Divisibility of positive mixed numbers – medium 583.9 kB 786 October 13, 2012
Divisibility of positive mixed numbers – hard 612.3 kB 805 October 13, 2012
Positive improper fractions
Divisibility of positive improper fractions – very easy 170.5 kB 802 October 13, 2012
Divisibility of positive improper fractions – easy 564.5 kB 778 October 13, 2012
Divisibility of positive improper fractions – medium 564.4 kB 741 October 13, 2012
Divisibility of positive improper fractions – hard 574.6 kB 797 October 13, 2012
Divisibility of positive improper fractions – very hard 574.1 kB 757 October 13, 2012
Non positive integers
Divisibility of integers – very easy 82.3 kB 874 October 13, 2012
Divisibility of integers – easy 154.6 kB 965 October 13, 2012
Divisibility of integers – medium 163.2 kB 1180 October 13, 2012
Divisibility of integers – hard 173.4 kB 1199 October 13, 2012
Non positive decimals
Divisibility of decimals – very easy 567.8 kB 852 October 13, 2012
Divisibility of decimals – easy 559.9 kB 885 October 13, 2012
Divisibility of decimals – medium 557 kB 812 October 13, 2012
Divisibility of decimals – hard 559.6 kB 1002 October 13, 2012
Non positive fractions
Divisibility of fractions – very easy 552.2 kB 831 October 13, 2012
Divisibility of fractions – easy 569.2 kB 831 October 13, 2012
Divisibility of fractions – medium 571.5 kB 787 October 13, 2012
Divisibility of fractions – hard 595.4 kB 817 October 13, 2012
Non positive mixed numbers
Divisibility of mixed numbers – easy 559.7 kB 788 October 13, 2012
Divisibility of mixed numbers – medium 588.7 kB 795 October 13, 2012
Divisibility of mixed numbers – hard 585.2 kB 756 October 13, 2012
Non positive improper fractions
Divisibility of improper fractions – easy 175 kB 954 October 13, 2012
Divisibility of improper fractions – medium 183.4 kB 877 October 13, 2012
Divisibility of improper fractions – hard 212.8 kB 1101 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 1908 October 13, 2012
Factoring numbers without exponents 125.7 kB 1182 October 13, 2012
Factoring with exponents 129.8 kB 1385 October 13, 2012


Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 137.7 kB 1484 October 14, 2012
Divisibility of positive decimals 192.9 kB 937 October 14, 2012
Divisibility of positive fractions 252.6 kB 810 October 14, 2012
Divisibility of positive mixed numbers 227 kB 765 October 14, 2012
Divisibility of positive improper fractions 248.8 kB 806 October 14, 2012
Non positive
Divisibility of integers 143.7 kB 957 October 14, 2012
Divisibility of decimals 222.3 kB 838 October 14, 2012
Divisibility of fractions 260.9 kB 891 October 14, 2012
Divisibility of mixed numbers 276.9 kB 797 October 14, 2012
Divisibility of improper fractions 234.4 kB 812 October 14, 2012
Factoring numbers
Factoring 198.2 kB 1510 October 14, 2012


Divisibility knowledge test