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 0 B 4151 January 1, 1970
Divisibility of positive integers – easy 0 B 2928 January 1, 1970
Divisibility of positive integers – medium 0 B 3595 January 1, 1970
Divisibility of positive integers – hard 0 B 2773 January 1, 1970
Positive decimals
Divisibility of positive decimals – very easy 0 B 1362 January 1, 1970
Divisibility of positive decimals – easy 0 B 1253 January 1, 1970
Divisibility of positive decimals – medium 0 B 1251 January 1, 1970
Divisibility of positive decimals – hard 0 B 1292 January 1, 1970
Positive fractions
Divisibility of positive fractions – very easy 0 B 1330 January 1, 1970
Divisibility of positive fractions – easy 0 B 1186 January 1, 1970
Divisibility of positive fractions – medium 0 B 1308 January 1, 1970
Divisibility of positive fractions – hard 0 B 1105 January 1, 1970
Positive mixed numbers
Divisibility of positive mixed numbers – easy 0 B 1208 January 1, 1970
Divisibility of positive mixed numbers – medium 0 B 1084 January 1, 1970
Divisibility of positive mixed numbers – hard 0 B 1036 January 1, 1970
Positive improper fractions
Divisibility of positive improper fractions – very easy 0 B 1068 January 1, 1970
Divisibility of positive improper fractions – easy 0 B 1011 January 1, 1970
Divisibility of positive improper fractions – medium 0 B 980 January 1, 1970
Divisibility of positive improper fractions – hard 0 B 1075 January 1, 1970
Divisibility of positive improper fractions – very hard 0 B 980 January 1, 1970
Non positive integers
Divisibility of integers – very easy 0 B 1233 January 1, 1970
Divisibility of integers – easy 0 B 1258 January 1, 1970
Divisibility of integers – medium 0 B 1496 January 1, 1970
Divisibility of integers – hard 0 B 1613 January 1, 1970
Non positive decimals
Divisibility of decimals – very easy 0 B 1097 January 1, 1970
Divisibility of decimals – easy 0 B 1220 January 1, 1970
Divisibility of decimals – medium 0 B 1047 January 1, 1970
Divisibility of decimals – hard 0 B 1349 January 1, 1970
Non positive fractions
Divisibility of fractions – very easy 0 B 1088 January 1, 1970
Divisibility of fractions – easy 0 B 1145 January 1, 1970
Divisibility of fractions – medium 0 B 1047 January 1, 1970
Divisibility of fractions – hard 0 B 1132 January 1, 1970
Non positive mixed numbers
Divisibility of mixed numbers – easy 0 B 1120 January 1, 1970
Divisibility of mixed numbers – medium 0 B 1087 January 1, 1970
Divisibility of mixed numbers – hard 0 B 1012 January 1, 1970
Non positive improper fractions
Divisibility of improper fractions – easy 0 B 1316 January 1, 1970
Divisibility of improper fractions – medium 0 B 1205 January 1, 1970
Divisibility of improper fractions – hard 0 B 1375 January 1, 1970

 

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 0 B 2449 January 1, 1970
Factoring numbers without exponents 0 B 1533 January 1, 1970
Factoring with exponents 0 B 2047 January 1, 1970


Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 0 B 1925 January 1, 1970
Divisibility of positive decimals 0 B 1243 January 1, 1970
Divisibility of positive fractions 0 B 1074 January 1, 1970
Divisibility of positive mixed numbers 0 B 998 January 1, 1970
Divisibility of positive improper fractions 0 B 1073 January 1, 1970
Non positive
Divisibility of integers 0 B 1304 January 1, 1970
Divisibility of decimals 0 B 1123 January 1, 1970
Divisibility of fractions 0 B 1165 January 1, 1970
Divisibility of mixed numbers 0 B 1035 January 1, 1970
Divisibility of improper fractions 0 B 1109 January 1, 1970
Factoring numbers
Factoring 0 B 2132 January 1, 1970


Divisibility knowledge test