# 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 107.1 kB 5760 September 3, 2019 Divisibility of positive integers – easy 157.4 kB 4123 September 3, 2019 Divisibility of positive integers – medium 164.8 kB 5005 September 3, 2019 Divisibility of positive integers – hard 179.1 kB 4287 September 3, 2019 Positive decimals Divisibility of positive decimals – very easy 559.2 kB 2247 September 3, 2019 Divisibility of positive decimals – easy 572.4 kB 2408 September 3, 2019 Divisibility of positive decimals – medium 575.7 kB 2349 September 3, 2019 Divisibility of positive decimals – hard 561.3 kB 2260 September 3, 2019 Positive fractions Divisibility of positive fractions – very easy 119 kB 2404 September 3, 2019 Divisibility of positive fractions – easy 564.6 kB 2009 September 3, 2019 Divisibility of positive fractions – medium 572.1 kB 2394 September 3, 2019 Divisibility of positive fractions – hard 576.9 kB 2060 September 3, 2019 Positive mixed numbers Divisibility of positive mixed numbers – easy 568.8 kB 2195 September 3, 2019 Divisibility of positive mixed numbers – medium 583.9 kB 2061 September 3, 2019 Divisibility of positive mixed numbers – hard 612.3 kB 1802 September 3, 2019 Positive improper fractions Divisibility of positive improper fractions – very easy 170.5 kB 2031 September 3, 2019 Divisibility of positive improper fractions – easy 564.5 kB 1915 September 3, 2019 Divisibility of positive improper fractions – medium 564.4 kB 1849 September 3, 2019 Divisibility of positive improper fractions – hard 574.6 kB 1851 September 3, 2019 Divisibility of positive improper fractions – very hard 574.1 kB 1877 September 3, 2019 Non positive integers Divisibility of integers – very easy 82.3 kB 2250 September 3, 2019 Divisibility of integers – easy 154.6 kB 2119 September 3, 2019 Divisibility of integers – medium 163.2 kB 2554 September 3, 2019 Divisibility of integers – hard 173.4 kB 2673 September 3, 2019 Non positive decimals Divisibility of decimals – very easy 567.8 kB 1960 September 3, 2019 Divisibility of decimals – easy 559.9 kB 2284 September 3, 2019 Divisibility of decimals – medium 557 kB 1846 September 3, 2019 Divisibility of decimals – hard 559.6 kB 2267 September 3, 2019 Non positive fractions Divisibility of fractions – very easy 552.2 kB 2053 September 3, 2019 Divisibility of fractions – easy 569.2 kB 2129 September 3, 2019 Divisibility of fractions – medium 571.5 kB 1983 September 3, 2019 Divisibility of fractions – hard 595.4 kB 2066 September 3, 2019 Non positive mixed numbers Divisibility of mixed numbers – easy 559.7 kB 2053 September 3, 2019 Divisibility of mixed numbers – medium 588.7 kB 1810 September 3, 2019 Divisibility of mixed numbers – hard 585.2 kB 1963 September 3, 2019 Non positive improper fractions Divisibility of improper fractions – easy 175 kB 2095 September 3, 2019 Divisibility of improper fractions – medium 183.4 kB 2184 September 3, 2019 Divisibility of improper fractions – hard 212.8 kB 2299 September 3, 2019

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 119.1 kB 3628 September 3, 2019 Factoring numbers without exponents 125.7 kB 2936 September 3, 2019 Factoring with exponents 129.8 kB 2982 September 3, 2019

## Divisibility and factoring worksheets for students

 Worksheet Name File Size Downloads Upload date Positive Divisibility of positive integers 137.7 kB 3119 September 3, 2019 Divisibility of positive decimals 192.9 kB 2093 September 3, 2019 Divisibility of positive fractions 252.6 kB 2003 September 3, 2019 Divisibility of positive mixed numbers 227 kB 1914 September 3, 2019 Divisibility of positive improper fractions 248.8 kB 1912 September 3, 2019 Non positive Divisibility of integers 143.7 kB 2303 September 3, 2019 Divisibility of decimals 222.3 kB 1983 September 3, 2019 Divisibility of fractions 260.9 kB 2084 September 3, 2019 Divisibility of mixed numbers 276.9 kB 1745 September 3, 2019 Divisibility of improper fractions 234.4 kB 1733 September 3, 2019 Factoring numbers Factoring 198.2 kB 3300 September 3, 2019