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 4541 January 1, 1970
Divisibility of positive integers – easy 0 B 3242 January 1, 1970
Divisibility of positive integers – medium 0 B 3888 January 1, 1970
Divisibility of positive integers – hard 0 B 3021 January 1, 1970
Positive decimals
Divisibility of positive decimals – very easy 0 B 1544 January 1, 1970
Divisibility of positive decimals – easy 0 B 1494 January 1, 1970
Divisibility of positive decimals – medium 0 B 1427 January 1, 1970
Divisibility of positive decimals – hard 0 B 1444 January 1, 1970
Positive fractions
Divisibility of positive fractions – very easy 0 B 1490 January 1, 1970
Divisibility of positive fractions – easy 0 B 1344 January 1, 1970
Divisibility of positive fractions – medium 0 B 1486 January 1, 1970
Divisibility of positive fractions – hard 0 B 1251 January 1, 1970
Positive mixed numbers
Divisibility of positive mixed numbers – easy 0 B 1377 January 1, 1970
Divisibility of positive mixed numbers – medium 0 B 1240 January 1, 1970
Divisibility of positive mixed numbers – hard 0 B 1189 January 1, 1970
Positive improper fractions
Divisibility of positive improper fractions – very easy 0 B 1240 January 1, 1970
Divisibility of positive improper fractions – easy 0 B 1152 January 1, 1970
Divisibility of positive improper fractions – medium 0 B 1110 January 1, 1970
Divisibility of positive improper fractions – hard 0 B 1229 January 1, 1970
Divisibility of positive improper fractions – very hard 0 B 1123 January 1, 1970
Non positive integers
Divisibility of integers – very easy 0 B 1415 January 1, 1970
Divisibility of integers – easy 0 B 1412 January 1, 1970
Divisibility of integers – medium 0 B 1661 January 1, 1970
Divisibility of integers – hard 0 B 1757 January 1, 1970
Non positive decimals
Divisibility of decimals – very easy 0 B 1254 January 1, 1970
Divisibility of decimals – easy 0 B 1392 January 1, 1970
Divisibility of decimals – medium 0 B 1202 January 1, 1970
Divisibility of decimals – hard 0 B 1496 January 1, 1970
Non positive fractions
Divisibility of fractions – very easy 0 B 1230 January 1, 1970
Divisibility of fractions – easy 0 B 1301 January 1, 1970
Divisibility of fractions – medium 0 B 1194 January 1, 1970
Divisibility of fractions – hard 0 B 1279 January 1, 1970
Non positive mixed numbers
Divisibility of mixed numbers – easy 0 B 1267 January 1, 1970
Divisibility of mixed numbers – medium 0 B 1235 January 1, 1970
Divisibility of mixed numbers – hard 0 B 1154 January 1, 1970
Non positive improper fractions
Divisibility of improper fractions – easy 0 B 1466 January 1, 1970
Divisibility of improper fractions – medium 0 B 1353 January 1, 1970
Divisibility of improper fractions – hard 0 B 1520 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 2697 January 1, 1970
Factoring numbers without exponents 0 B 1669 January 1, 1970
Factoring with exponents 0 B 2331 January 1, 1970

Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 0 B 2133 January 1, 1970
Divisibility of positive decimals 0 B 1390 January 1, 1970
Divisibility of positive fractions 0 B 1207 January 1, 1970
Divisibility of positive mixed numbers 0 B 1137 January 1, 1970
Divisibility of positive improper fractions 0 B 1195 January 1, 1970
Non positive
Divisibility of integers 0 B 1443 January 1, 1970
Divisibility of decimals 0 B 1260 January 1, 1970
Divisibility of fractions 0 B 1291 January 1, 1970
Divisibility of mixed numbers 0 B 1157 January 1, 1970
Divisibility of improper fractions 0 B 1221 January 1, 1970
Factoring numbers
Factoring 0 B 2467 January 1, 1970

Divisibility knowledge test