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.
Divisibility exams for teachers
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  2171  October 13, 2012 
Factoring numbers without exponents  125.7 kB  1301  October 13, 2012 
Factoring with exponents  129.8 kB  1718  October 13, 2012 
Divisibility and factoring worksheets for students
Worksheet Name  File Size  Downloads  Upload date 
Positive


Divisibility of positive integers  137.7 kB  1735  October 14, 2012 
Divisibility of positive decimals  192.9 kB  1097  October 14, 2012 
Divisibility of positive fractions  252.6 kB  926  October 14, 2012 
Divisibility of positive mixed numbers  227 kB  882  October 14, 2012 
Divisibility of positive improper fractions  248.8 kB  947  October 14, 2012 
Non positive


Divisibility of integers  143.7 kB  1158  October 14, 2012 
Divisibility of decimals  222.3 kB  954  October 14, 2012 
Divisibility of fractions  260.9 kB  1029  October 14, 2012 
Divisibility of mixed numbers  276.9 kB  894  October 14, 2012 
Divisibility of improper fractions  234.4 kB  986  October 14, 2012 
Factoring numbers


Factoring  198.2 kB  1781  October 14, 2012 