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 4221 January 1, 1970
Divisibility of positive integers – easy 0 B 2992 January 1, 1970
Divisibility of positive integers – medium 0 B 3640 January 1, 1970
Divisibility of positive integers – hard 0 B 2818 January 1, 1970
Positive decimals
Divisibility of positive decimals – very easy 0 B 1387 January 1, 1970
Divisibility of positive decimals – easy 0 B 1294 January 1, 1970
Divisibility of positive decimals – medium 0 B 1272 January 1, 1970
Divisibility of positive decimals – hard 0 B 1314 January 1, 1970
Positive fractions
Divisibility of positive fractions – very easy 0 B 1361 January 1, 1970
Divisibility of positive fractions – easy 0 B 1211 January 1, 1970
Divisibility of positive fractions – medium 0 B 1339 January 1, 1970
Divisibility of positive fractions – hard 0 B 1127 January 1, 1970
Positive mixed numbers
Divisibility of positive mixed numbers – easy 0 B 1239 January 1, 1970
Divisibility of positive mixed numbers – medium 0 B 1108 January 1, 1970
Divisibility of positive mixed numbers – hard 0 B 1057 January 1, 1970
Positive improper fractions
Divisibility of positive improper fractions – very easy 0 B 1106 January 1, 1970
Divisibility of positive improper fractions – easy 0 B 1031 January 1, 1970
Divisibility of positive improper fractions – medium 0 B 1001 January 1, 1970
Divisibility of positive improper fractions – hard 0 B 1103 January 1, 1970
Divisibility of positive improper fractions – very hard 0 B 1006 January 1, 1970
Non positive integers
Divisibility of integers – very easy 0 B 1266 January 1, 1970
Divisibility of integers – easy 0 B 1282 January 1, 1970
Divisibility of integers – medium 0 B 1525 January 1, 1970
Divisibility of integers – hard 0 B 1635 January 1, 1970
Non positive decimals
Divisibility of decimals – very easy 0 B 1119 January 1, 1970
Divisibility of decimals – easy 0 B 1243 January 1, 1970
Divisibility of decimals – medium 0 B 1070 January 1, 1970
Divisibility of decimals – hard 0 B 1368 January 1, 1970
Non positive fractions
Divisibility of fractions – very easy 0 B 1107 January 1, 1970
Divisibility of fractions – easy 0 B 1166 January 1, 1970
Divisibility of fractions – medium 0 B 1067 January 1, 1970
Divisibility of fractions – hard 0 B 1153 January 1, 1970
Non positive mixed numbers
Divisibility of mixed numbers – easy 0 B 1144 January 1, 1970
Divisibility of mixed numbers – medium 0 B 1104 January 1, 1970
Divisibility of mixed numbers – hard 0 B 1032 January 1, 1970
Non positive improper fractions
Divisibility of improper fractions – easy 0 B 1333 January 1, 1970
Divisibility of improper fractions – medium 0 B 1237 January 1, 1970
Divisibility of improper fractions – hard 0 B 1398 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 2499 January 1, 1970
Factoring numbers without exponents 0 B 1563 January 1, 1970
Factoring with exponents 0 B 2103 January 1, 1970


Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 0 B 1957 January 1, 1970
Divisibility of positive decimals 0 B 1269 January 1, 1970
Divisibility of positive fractions 0 B 1095 January 1, 1970
Divisibility of positive mixed numbers 0 B 1016 January 1, 1970
Divisibility of positive improper fractions 0 B 1093 January 1, 1970
Non positive
Divisibility of integers 0 B 1324 January 1, 1970
Divisibility of decimals 0 B 1145 January 1, 1970
Divisibility of fractions 0 B 1188 January 1, 1970
Divisibility of mixed numbers 0 B 1056 January 1, 1970
Divisibility of improper fractions 0 B 1131 January 1, 1970
Factoring numbers
Factoring 0 B 2177 January 1, 1970


Divisibility knowledge test