# 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. ## Divisibility exams for teachers

 Exam Name File Size Downloads Upload date Positive integers Divisibility of positive integers – very easy 0 B 4392 January 1, 1970 Divisibility of positive integers – easy 0 B 3123 January 1, 1970 Divisibility of positive integers – medium 0 B 3755 January 1, 1970 Divisibility of positive integers – hard 0 B 2920 January 1, 1970 Positive decimals Divisibility of positive decimals – very easy 0 B 1462 January 1, 1970 Divisibility of positive decimals – easy 0 B 1398 January 1, 1970 Divisibility of positive decimals – medium 0 B 1336 January 1, 1970 Divisibility of positive decimals – hard 0 B 1372 January 1, 1970 Positive fractions Divisibility of positive fractions – very easy 0 B 1424 January 1, 1970 Divisibility of positive fractions – easy 0 B 1270 January 1, 1970 Divisibility of positive fractions – medium 0 B 1399 January 1, 1970 Divisibility of positive fractions – hard 0 B 1181 January 1, 1970 Positive mixed numbers Divisibility of positive mixed numbers – easy 0 B 1308 January 1, 1970 Divisibility of positive mixed numbers – medium 0 B 1170 January 1, 1970 Divisibility of positive mixed numbers – hard 0 B 1113 January 1, 1970 Positive improper fractions Divisibility of positive improper fractions – very easy 0 B 1176 January 1, 1970 Divisibility of positive improper fractions – easy 0 B 1083 January 1, 1970 Divisibility of positive improper fractions – medium 0 B 1046 January 1, 1970 Divisibility of positive improper fractions – hard 0 B 1158 January 1, 1970 Divisibility of positive improper fractions – very hard 0 B 1052 January 1, 1970 Non positive integers Divisibility of integers – very easy 0 B 1338 January 1, 1970 Divisibility of integers – easy 0 B 1348 January 1, 1970 Divisibility of integers – medium 0 B 1593 January 1, 1970 Divisibility of integers – hard 0 B 1698 January 1, 1970 Non positive decimals Divisibility of decimals – very easy 0 B 1180 January 1, 1970 Divisibility of decimals – easy 0 B 1312 January 1, 1970 Divisibility of decimals – medium 0 B 1126 January 1, 1970 Divisibility of decimals – hard 0 B 1425 January 1, 1970 Non positive fractions Divisibility of fractions – very easy 0 B 1161 January 1, 1970 Divisibility of fractions – easy 0 B 1234 January 1, 1970 Divisibility of fractions – medium 0 B 1127 January 1, 1970 Divisibility of fractions – hard 0 B 1209 January 1, 1970 Non positive mixed numbers Divisibility of mixed numbers – easy 0 B 1201 January 1, 1970 Divisibility of mixed numbers – medium 0 B 1166 January 1, 1970 Divisibility of mixed numbers – hard 0 B 1086 January 1, 1970 Non positive improper fractions Divisibility of improper fractions – easy 0 B 1396 January 1, 1970 Divisibility of improper fractions – medium 0 B 1300 January 1, 1970 Divisibility of improper fractions – hard 0 B 1453 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 2608 January 1, 1970 Factoring numbers without exponents 0 B 1609 January 1, 1970 Factoring with exponents 0 B 2239 January 1, 1970

## Divisibility and factoring worksheets for students

 Worksheet Name File Size Downloads Upload date Positive Divisibility of positive integers 0 B 2029 January 1, 1970 Divisibility of positive decimals 0 B 1318 January 1, 1970 Divisibility of positive fractions 0 B 1145 January 1, 1970 Divisibility of positive mixed numbers 0 B 1071 January 1, 1970 Divisibility of positive improper fractions 0 B 1132 January 1, 1970 Non positive Divisibility of integers 0 B 1377 January 1, 1970 Divisibility of decimals 0 B 1199 January 1, 1970 Divisibility of fractions 0 B 1234 January 1, 1970 Divisibility of mixed numbers 0 B 1099 January 1, 1970 Divisibility of improper fractions 0 B 1169 January 1, 1970 Factoring numbers Factoring 0 B 2375 January 1, 1970