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 4264 January 1, 1970
Divisibility of positive integers – easy 0 B 3037 January 1, 1970
Divisibility of positive integers – medium 0 B 3669 January 1, 1970
Divisibility of positive integers – hard 0 B 2848 January 1, 1970
Positive decimals
Divisibility of positive decimals – very easy 0 B 1410 January 1, 1970
Divisibility of positive decimals – easy 0 B 1324 January 1, 1970
Divisibility of positive decimals – medium 0 B 1286 January 1, 1970
Divisibility of positive decimals – hard 0 B 1332 January 1, 1970
Positive fractions
Divisibility of positive fractions – very easy 0 B 1376 January 1, 1970
Divisibility of positive fractions – easy 0 B 1225 January 1, 1970
Divisibility of positive fractions – medium 0 B 1355 January 1, 1970
Divisibility of positive fractions – hard 0 B 1141 January 1, 1970
Positive mixed numbers
Divisibility of positive mixed numbers – easy 0 B 1256 January 1, 1970
Divisibility of positive mixed numbers – medium 0 B 1124 January 1, 1970
Divisibility of positive mixed numbers – hard 0 B 1071 January 1, 1970
Positive improper fractions
Divisibility of positive improper fractions – very easy 0 B 1134 January 1, 1970
Divisibility of positive improper fractions – easy 0 B 1043 January 1, 1970
Divisibility of positive improper fractions – medium 0 B 1014 January 1, 1970
Divisibility of positive improper fractions – hard 0 B 1115 January 1, 1970
Divisibility of positive improper fractions – very hard 0 B 1016 January 1, 1970
Non positive integers
Divisibility of integers – very easy 0 B 1284 January 1, 1970
Divisibility of integers – easy 0 B 1293 January 1, 1970
Divisibility of integers – medium 0 B 1543 January 1, 1970
Divisibility of integers – hard 0 B 1652 January 1, 1970
Non positive decimals
Divisibility of decimals – very easy 0 B 1132 January 1, 1970
Divisibility of decimals – easy 0 B 1257 January 1, 1970
Divisibility of decimals – medium 0 B 1085 January 1, 1970
Divisibility of decimals – hard 0 B 1382 January 1, 1970
Non positive fractions
Divisibility of fractions – very easy 0 B 1121 January 1, 1970
Divisibility of fractions – easy 0 B 1180 January 1, 1970
Divisibility of fractions – medium 0 B 1083 January 1, 1970
Divisibility of fractions – hard 0 B 1168 January 1, 1970
Non positive mixed numbers
Divisibility of mixed numbers – easy 0 B 1161 January 1, 1970
Divisibility of mixed numbers – medium 0 B 1118 January 1, 1970
Divisibility of mixed numbers – hard 0 B 1048 January 1, 1970
Non positive improper fractions
Divisibility of improper fractions – easy 0 B 1350 January 1, 1970
Divisibility of improper fractions – medium 0 B 1257 January 1, 1970
Divisibility of improper fractions – hard 0 B 1412 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 2534 January 1, 1970
Factoring numbers without exponents 0 B 1579 January 1, 1970
Factoring with exponents 0 B 2156 January 1, 1970


Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 0 B 1981 January 1, 1970
Divisibility of positive decimals 0 B 1284 January 1, 1970
Divisibility of positive fractions 0 B 1110 January 1, 1970
Divisibility of positive mixed numbers 0 B 1034 January 1, 1970
Divisibility of positive improper fractions 0 B 1106 January 1, 1970
Non positive
Divisibility of integers 0 B 1341 January 1, 1970
Divisibility of decimals 0 B 1159 January 1, 1970
Divisibility of fractions 0 B 1200 January 1, 1970
Divisibility of mixed numbers 0 B 1067 January 1, 1970
Divisibility of improper fractions 0 B 1143 January 1, 1970
Factoring numbers
Factoring 0 B 2230 January 1, 1970


Divisibility knowledge test