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 4307 January 1, 1970
Divisibility of positive integers – easy 0 B 3064 January 1, 1970
Divisibility of positive integers – medium 0 B 3699 January 1, 1970
Divisibility of positive integers – hard 0 B 2870 January 1, 1970
Positive decimals
Divisibility of positive decimals – very easy 0 B 1426 January 1, 1970
Divisibility of positive decimals – easy 0 B 1355 January 1, 1970
Divisibility of positive decimals – medium 0 B 1304 January 1, 1970
Divisibility of positive decimals – hard 0 B 1347 January 1, 1970
Positive fractions
Divisibility of positive fractions – very easy 0 B 1393 January 1, 1970
Divisibility of positive fractions – easy 0 B 1238 January 1, 1970
Divisibility of positive fractions – medium 0 B 1366 January 1, 1970
Divisibility of positive fractions – hard 0 B 1151 January 1, 1970
Positive mixed numbers
Divisibility of positive mixed numbers – easy 0 B 1273 January 1, 1970
Divisibility of positive mixed numbers – medium 0 B 1138 January 1, 1970
Divisibility of positive mixed numbers – hard 0 B 1081 January 1, 1970
Positive improper fractions
Divisibility of positive improper fractions – very easy 0 B 1148 January 1, 1970
Divisibility of positive improper fractions – easy 0 B 1054 January 1, 1970
Divisibility of positive improper fractions – medium 0 B 1024 January 1, 1970
Divisibility of positive improper fractions – hard 0 B 1128 January 1, 1970
Divisibility of positive improper fractions – very hard 0 B 1027 January 1, 1970
Non positive integers
Divisibility of integers – very easy 0 B 1300 January 1, 1970
Divisibility of integers – easy 0 B 1313 January 1, 1970
Divisibility of integers – medium 0 B 1561 January 1, 1970
Divisibility of integers – hard 0 B 1665 January 1, 1970
Non positive decimals
Divisibility of decimals – very easy 0 B 1150 January 1, 1970
Divisibility of decimals – easy 0 B 1280 January 1, 1970
Divisibility of decimals – medium 0 B 1099 January 1, 1970
Divisibility of decimals – hard 0 B 1394 January 1, 1970
Non positive fractions
Divisibility of fractions – very easy 0 B 1133 January 1, 1970
Divisibility of fractions – easy 0 B 1193 January 1, 1970
Divisibility of fractions – medium 0 B 1097 January 1, 1970
Divisibility of fractions – hard 0 B 1180 January 1, 1970
Non positive mixed numbers
Divisibility of mixed numbers – easy 0 B 1175 January 1, 1970
Divisibility of mixed numbers – medium 0 B 1134 January 1, 1970
Divisibility of mixed numbers – hard 0 B 1062 January 1, 1970
Non positive improper fractions
Divisibility of improper fractions – easy 0 B 1366 January 1, 1970
Divisibility of improper fractions – medium 0 B 1270 January 1, 1970
Divisibility of improper fractions – hard 0 B 1426 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 2558 January 1, 1970
Factoring numbers without exponents 0 B 1587 January 1, 1970
Factoring with exponents 0 B 2182 January 1, 1970

Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 0 B 1995 January 1, 1970
Divisibility of positive decimals 0 B 1295 January 1, 1970
Divisibility of positive fractions 0 B 1116 January 1, 1970
Divisibility of positive mixed numbers 0 B 1044 January 1, 1970
Divisibility of positive improper fractions 0 B 1111 January 1, 1970
Non positive
Divisibility of integers 0 B 1348 January 1, 1970
Divisibility of decimals 0 B 1173 January 1, 1970
Divisibility of fractions 0 B 1208 January 1, 1970
Divisibility of mixed numbers 0 B 1079 January 1, 1970
Divisibility of improper fractions 0 B 1150 January 1, 1970
Factoring numbers
Factoring 0 B 2257 January 1, 1970

Divisibility knowledge test