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 3977 January 1, 1970
Divisibility of positive integers – easy 0 B 2823 January 1, 1970
Divisibility of positive integers – medium 0 B 3494 January 1, 1970
Divisibility of positive integers – hard 0 B 2691 January 1, 1970
Positive decimals
Divisibility of positive decimals – very easy 0 B 1300 January 1, 1970
Divisibility of positive decimals – easy 0 B 1192 January 1, 1970
Divisibility of positive decimals – medium 0 B 1198 January 1, 1970
Divisibility of positive decimals – hard 0 B 1231 January 1, 1970
Positive fractions
Divisibility of positive fractions – very easy 0 B 1276 January 1, 1970
Divisibility of positive fractions – easy 0 B 1136 January 1, 1970
Divisibility of positive fractions – medium 0 B 1241 January 1, 1970
Divisibility of positive fractions – hard 0 B 1054 January 1, 1970
Positive mixed numbers
Divisibility of positive mixed numbers – easy 0 B 1168 January 1, 1970
Divisibility of positive mixed numbers – medium 0 B 1024 January 1, 1970
Divisibility of positive mixed numbers – hard 0 B 991 January 1, 1970
Positive improper fractions
Divisibility of positive improper fractions – very easy 0 B 1023 January 1, 1970
Divisibility of positive improper fractions – easy 0 B 975 January 1, 1970
Divisibility of positive improper fractions – medium 0 B 935 January 1, 1970
Divisibility of positive improper fractions – hard 0 B 1030 January 1, 1970
Divisibility of positive improper fractions – very hard 0 B 925 January 1, 1970
Non positive integers
Divisibility of integers – very easy 0 B 1170 January 1, 1970
Divisibility of integers – easy 0 B 1214 January 1, 1970
Divisibility of integers – medium 0 B 1455 January 1, 1970
Divisibility of integers – hard 0 B 1550 January 1, 1970
Non positive decimals
Divisibility of decimals – very easy 0 B 1051 January 1, 1970
Divisibility of decimals – easy 0 B 1169 January 1, 1970
Divisibility of decimals – medium 0 B 1008 January 1, 1970
Divisibility of decimals – hard 0 B 1301 January 1, 1970
Non positive fractions
Divisibility of fractions – very easy 0 B 1043 January 1, 1970
Divisibility of fractions – easy 0 B 1097 January 1, 1970
Divisibility of fractions – medium 0 B 998 January 1, 1970
Divisibility of fractions – hard 0 B 1071 January 1, 1970
Non positive mixed numbers
Divisibility of mixed numbers – easy 0 B 1071 January 1, 1970
Divisibility of mixed numbers – medium 0 B 1032 January 1, 1970
Divisibility of mixed numbers – hard 0 B 966 January 1, 1970
Non positive improper fractions
Divisibility of improper fractions – easy 0 B 1271 January 1, 1970
Divisibility of improper fractions – medium 0 B 1152 January 1, 1970
Divisibility of improper fractions – hard 0 B 1328 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 2342 January 1, 1970
Factoring numbers without exponents 0 B 1473 January 1, 1970
Factoring with exponents 0 B 1927 January 1, 1970


Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 0 B 1849 January 1, 1970
Divisibility of positive decimals 0 B 1201 January 1, 1970
Divisibility of positive fractions 0 B 1029 January 1, 1970
Divisibility of positive mixed numbers 0 B 958 January 1, 1970
Divisibility of positive improper fractions 0 B 1033 January 1, 1970
Non positive
Divisibility of integers 0 B 1260 January 1, 1970
Divisibility of decimals 0 B 1081 January 1, 1970
Divisibility of fractions 0 B 1122 January 1, 1970
Divisibility of mixed numbers 0 B 986 January 1, 1970
Divisibility of improper fractions 0 B 1069 January 1, 1970
Factoring numbers
Factoring 0 B 2023 January 1, 1970


Divisibility knowledge test