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 107.1 kB 5938 September 3, 2019
Divisibility of positive integers – easy 157.4 kB 4285 September 3, 2019
Divisibility of positive integers – medium 164.8 kB 5170 September 3, 2019
Divisibility of positive integers – hard 179.1 kB 4440 September 3, 2019
Positive decimals
Divisibility of positive decimals – very easy 559.2 kB 2378 September 3, 2019
Divisibility of positive decimals – easy 572.4 kB 2537 September 3, 2019
Divisibility of positive decimals – medium 575.7 kB 2483 September 3, 2019
Divisibility of positive decimals – hard 561.3 kB 2387 September 3, 2019
Positive fractions
Divisibility of positive fractions – very easy 119 kB 2524 September 3, 2019
Divisibility of positive fractions – easy 564.6 kB 2127 September 3, 2019
Divisibility of positive fractions – medium 572.1 kB 2515 September 3, 2019
Divisibility of positive fractions – hard 576.9 kB 2173 September 3, 2019
Positive mixed numbers
Divisibility of positive mixed numbers – easy 568.8 kB 2309 September 3, 2019
Divisibility of positive mixed numbers – medium 583.9 kB 2252 September 3, 2019
Divisibility of positive mixed numbers – hard 612.3 kB 1917 September 3, 2019
Positive improper fractions
Divisibility of positive improper fractions – very easy 170.5 kB 2162 September 3, 2019
Divisibility of positive improper fractions – easy 564.5 kB 2030 September 3, 2019
Divisibility of positive improper fractions – medium 564.4 kB 1966 September 3, 2019
Divisibility of positive improper fractions – hard 574.6 kB 1971 September 3, 2019
Divisibility of positive improper fractions – very hard 574.1 kB 1994 September 3, 2019
Non positive integers
Divisibility of integers – very easy 82.3 kB 2380 September 3, 2019
Divisibility of integers – easy 154.6 kB 2235 September 3, 2019
Divisibility of integers – medium 163.2 kB 2757 September 3, 2019
Divisibility of integers – hard 173.4 kB 2809 September 3, 2019
Non positive decimals
Divisibility of decimals – very easy 567.8 kB 2107 September 3, 2019
Divisibility of decimals – easy 559.9 kB 2427 September 3, 2019
Divisibility of decimals – medium 557 kB 1972 September 3, 2019
Divisibility of decimals – hard 559.6 kB 2393 September 3, 2019
Non positive fractions
Divisibility of fractions – very easy 552.2 kB 2174 September 3, 2019
Divisibility of fractions – easy 569.2 kB 2267 September 3, 2019
Divisibility of fractions – medium 571.5 kB 2123 September 3, 2019
Divisibility of fractions – hard 595.4 kB 2178 September 3, 2019
Non positive mixed numbers
Divisibility of mixed numbers – easy 559.7 kB 2175 September 3, 2019
Divisibility of mixed numbers – medium 588.7 kB 1930 September 3, 2019
Divisibility of mixed numbers – hard 585.2 kB 2077 September 3, 2019
Non positive improper fractions
Divisibility of improper fractions – easy 175 kB 2206 September 3, 2019
Divisibility of improper fractions – medium 183.4 kB 2298 September 3, 2019
Divisibility of improper fractions – hard 212.8 kB 2421 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 3753 September 3, 2019
Factoring numbers without exponents 125.7 kB 3057 September 3, 2019
Factoring with exponents 129.8 kB 3092 September 3, 2019

Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 137.7 kB 3263 September 3, 2019
Divisibility of positive decimals 192.9 kB 2271 September 3, 2019
Divisibility of positive fractions 252.6 kB 2135 September 3, 2019
Divisibility of positive mixed numbers 227 kB 2027 September 3, 2019
Divisibility of positive improper fractions 248.8 kB 2021 September 3, 2019
Non positive
Divisibility of integers 143.7 kB 2423 September 3, 2019
Divisibility of decimals 222.3 kB 2120 September 3, 2019
Divisibility of fractions 260.9 kB 2222 September 3, 2019
Divisibility of mixed numbers 276.9 kB 1862 September 3, 2019
Divisibility of improper fractions 234.4 kB 1836 September 3, 2019
Factoring numbers
Factoring 198.2 kB 3454 September 3, 2019