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 4343 January 1, 1970
Divisibility of positive integers – easy 0 B 3091 January 1, 1970
Divisibility of positive integers – medium 0 B 3727 January 1, 1970
Divisibility of positive integers – hard 0 B 2894 January 1, 1970
Positive decimals
Divisibility of positive decimals – very easy 0 B 1439 January 1, 1970
Divisibility of positive decimals – easy 0 B 1369 January 1, 1970
Divisibility of positive decimals – medium 0 B 1313 January 1, 1970
Divisibility of positive decimals – hard 0 B 1354 January 1, 1970
Positive fractions
Divisibility of positive fractions – very easy 0 B 1405 January 1, 1970
Divisibility of positive fractions – easy 0 B 1250 January 1, 1970
Divisibility of positive fractions – medium 0 B 1381 January 1, 1970
Divisibility of positive fractions – hard 0 B 1163 January 1, 1970
Positive mixed numbers
Divisibility of positive mixed numbers – easy 0 B 1287 January 1, 1970
Divisibility of positive mixed numbers – medium 0 B 1153 January 1, 1970
Divisibility of positive mixed numbers – hard 0 B 1091 January 1, 1970
Positive improper fractions
Divisibility of positive improper fractions – very easy 0 B 1159 January 1, 1970
Divisibility of positive improper fractions – easy 0 B 1064 January 1, 1970
Divisibility of positive improper fractions – medium 0 B 1031 January 1, 1970
Divisibility of positive improper fractions – hard 0 B 1141 January 1, 1970
Divisibility of positive improper fractions – very hard 0 B 1036 January 1, 1970
Non positive integers
Divisibility of integers – very easy 0 B 1316 January 1, 1970
Divisibility of integers – easy 0 B 1328 January 1, 1970
Divisibility of integers – medium 0 B 1573 January 1, 1970
Divisibility of integers – hard 0 B 1681 January 1, 1970
Non positive decimals
Divisibility of decimals – very easy 0 B 1162 January 1, 1970
Divisibility of decimals – easy 0 B 1293 January 1, 1970
Divisibility of decimals – medium 0 B 1108 January 1, 1970
Divisibility of decimals – hard 0 B 1401 January 1, 1970
Non positive fractions
Divisibility of fractions – very easy 0 B 1141 January 1, 1970
Divisibility of fractions – easy 0 B 1209 January 1, 1970
Divisibility of fractions – medium 0 B 1110 January 1, 1970
Divisibility of fractions – hard 0 B 1192 January 1, 1970
Non positive mixed numbers
Divisibility of mixed numbers – easy 0 B 1184 January 1, 1970
Divisibility of mixed numbers – medium 0 B 1145 January 1, 1970
Divisibility of mixed numbers – hard 0 B 1069 January 1, 1970
Non positive improper fractions
Divisibility of improper fractions – easy 0 B 1376 January 1, 1970
Divisibility of improper fractions – medium 0 B 1281 January 1, 1970
Divisibility of improper fractions – hard 0 B 1435 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 2578 January 1, 1970
Factoring numbers without exponents 0 B 1593 January 1, 1970
Factoring with exponents 0 B 2207 January 1, 1970

Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 0 B 2008 January 1, 1970
Divisibility of positive decimals 0 B 1302 January 1, 1970
Divisibility of positive fractions 0 B 1125 January 1, 1970
Divisibility of positive mixed numbers 0 B 1052 January 1, 1970
Divisibility of positive improper fractions 0 B 1120 January 1, 1970
Non positive
Divisibility of integers 0 B 1357 January 1, 1970
Divisibility of decimals 0 B 1179 January 1, 1970
Divisibility of fractions 0 B 1216 January 1, 1970
Divisibility of mixed numbers 0 B 1087 January 1, 1970
Divisibility of improper fractions 0 B 1155 January 1, 1970
Factoring numbers
Factoring 0 B 2319 January 1, 1970

Divisibility knowledge test