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 4108 January 1, 1970
Divisibility of positive integers – easy 0 B 2908 January 1, 1970
Divisibility of positive integers – medium 0 B 3573 January 1, 1970
Divisibility of positive integers – hard 0 B 2751 January 1, 1970
Positive decimals
Divisibility of positive decimals – very easy 0 B 1343 January 1, 1970
Divisibility of positive decimals – easy 0 B 1240 January 1, 1970
Divisibility of positive decimals – medium 0 B 1237 January 1, 1970
Divisibility of positive decimals – hard 0 B 1277 January 1, 1970
Positive fractions
Divisibility of positive fractions – very easy 0 B 1312 January 1, 1970
Divisibility of positive fractions – easy 0 B 1177 January 1, 1970
Divisibility of positive fractions – medium 0 B 1295 January 1, 1970
Divisibility of positive fractions – hard 0 B 1093 January 1, 1970
Positive mixed numbers
Divisibility of positive mixed numbers – easy 0 B 1198 January 1, 1970
Divisibility of positive mixed numbers – medium 0 B 1073 January 1, 1970
Divisibility of positive mixed numbers – hard 0 B 1028 January 1, 1970
Positive improper fractions
Divisibility of positive improper fractions – very easy 0 B 1057 January 1, 1970
Divisibility of positive improper fractions – easy 0 B 1004 January 1, 1970
Divisibility of positive improper fractions – medium 0 B 975 January 1, 1970
Divisibility of positive improper fractions – hard 0 B 1065 January 1, 1970
Divisibility of positive improper fractions – very hard 0 B 972 January 1, 1970
Non positive integers
Divisibility of integers – very easy 0 B 1222 January 1, 1970
Divisibility of integers – easy 0 B 1249 January 1, 1970
Divisibility of integers – medium 0 B 1487 January 1, 1970
Divisibility of integers – hard 0 B 1605 January 1, 1970
Non positive decimals
Divisibility of decimals – very easy 0 B 1085 January 1, 1970
Divisibility of decimals – easy 0 B 1211 January 1, 1970
Divisibility of decimals – medium 0 B 1038 January 1, 1970
Divisibility of decimals – hard 0 B 1342 January 1, 1970
Non positive fractions
Divisibility of fractions – very easy 0 B 1080 January 1, 1970
Divisibility of fractions – easy 0 B 1138 January 1, 1970
Divisibility of fractions – medium 0 B 1040 January 1, 1970
Divisibility of fractions – hard 0 B 1122 January 1, 1970
Non positive mixed numbers
Divisibility of mixed numbers – easy 0 B 1108 January 1, 1970
Divisibility of mixed numbers – medium 0 B 1078 January 1, 1970
Divisibility of mixed numbers – hard 0 B 1004 January 1, 1970
Non positive improper fractions
Divisibility of improper fractions – easy 0 B 1306 January 1, 1970
Divisibility of improper fractions – medium 0 B 1197 January 1, 1970
Divisibility of improper fractions – hard 0 B 1364 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 2430 January 1, 1970
Factoring numbers without exponents 0 B 1521 January 1, 1970
Factoring with exponents 0 B 2021 January 1, 1970


Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 0 B 1906 January 1, 1970
Divisibility of positive decimals 0 B 1234 January 1, 1970
Divisibility of positive fractions 0 B 1066 January 1, 1970
Divisibility of positive mixed numbers 0 B 993 January 1, 1970
Divisibility of positive improper fractions 0 B 1062 January 1, 1970
Non positive
Divisibility of integers 0 B 1296 January 1, 1970
Divisibility of decimals 0 B 1115 January 1, 1970
Divisibility of fractions 0 B 1156 January 1, 1970
Divisibility of mixed numbers 0 B 1028 January 1, 1970
Divisibility of improper fractions 0 B 1100 January 1, 1970
Factoring numbers
Factoring 0 B 2112 January 1, 1970


Divisibility knowledge test