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 6206 September 3, 2019
Divisibility of positive integers – easy 157.4 kB 4517 September 3, 2019
Divisibility of positive integers – medium 164.8 kB 5468 September 3, 2019
Divisibility of positive integers – hard 179.1 kB 4696 September 3, 2019
Positive decimals
Divisibility of positive decimals – very easy 559.2 kB 2620 September 3, 2019
Divisibility of positive decimals – easy 572.4 kB 2787 September 3, 2019
Divisibility of positive decimals – medium 575.7 kB 2728 September 3, 2019
Divisibility of positive decimals – hard 561.3 kB 2630 September 3, 2019
Positive fractions
Divisibility of positive fractions – very easy 119 kB 2756 September 3, 2019
Divisibility of positive fractions – easy 564.6 kB 2347 September 3, 2019
Divisibility of positive fractions – medium 572.1 kB 2746 September 3, 2019
Divisibility of positive fractions – hard 576.9 kB 2396 September 3, 2019
Positive mixed numbers
Divisibility of positive mixed numbers – easy 568.8 kB 2527 September 3, 2019
Divisibility of positive mixed numbers – medium 583.9 kB 2520 September 3, 2019
Divisibility of positive mixed numbers – hard 612.3 kB 2145 September 3, 2019
Positive improper fractions
Divisibility of positive improper fractions – very easy 170.5 kB 2372 September 3, 2019
Divisibility of positive improper fractions – easy 564.5 kB 2252 September 3, 2019
Divisibility of positive improper fractions – medium 564.4 kB 2189 September 3, 2019
Divisibility of positive improper fractions – hard 574.6 kB 2189 September 3, 2019
Divisibility of positive improper fractions – very hard 574.1 kB 2224 September 3, 2019
Non positive integers
Divisibility of integers – very easy 82.3 kB 2612 September 3, 2019
Divisibility of integers – easy 154.6 kB 2458 September 3, 2019
Divisibility of integers – medium 163.2 kB 3063 September 3, 2019
Divisibility of integers – hard 173.4 kB 3029 September 3, 2019
Non positive decimals
Divisibility of decimals – very easy 567.8 kB 2380 September 3, 2019
Divisibility of decimals – easy 559.9 kB 2690 September 3, 2019
Divisibility of decimals – medium 557 kB 2195 September 3, 2019
Divisibility of decimals – hard 559.6 kB 2620 September 3, 2019
Non positive fractions
Divisibility of fractions – very easy 552.2 kB 2383 September 3, 2019
Divisibility of fractions – easy 569.2 kB 2514 September 3, 2019
Divisibility of fractions – medium 571.5 kB 2391 September 3, 2019
Divisibility of fractions – hard 595.4 kB 2393 September 3, 2019
Non positive mixed numbers
Divisibility of mixed numbers – easy 559.7 kB 2389 September 3, 2019
Divisibility of mixed numbers – medium 588.7 kB 2152 September 3, 2019
Divisibility of mixed numbers – hard 585.2 kB 2299 September 3, 2019
Non positive improper fractions
Divisibility of improper fractions – easy 175 kB 2429 September 3, 2019
Divisibility of improper fractions – medium 183.4 kB 2550 September 3, 2019
Divisibility of improper fractions – hard 212.8 kB 2652 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 3995 September 3, 2019
Factoring numbers without exponents 125.7 kB 3295 September 3, 2019
Factoring with exponents 129.8 kB 3304 September 3, 2019

Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 137.7 kB 3523 September 3, 2019
Divisibility of positive decimals 192.9 kB 2514 September 3, 2019
Divisibility of positive fractions 252.6 kB 2368 September 3, 2019
Divisibility of positive mixed numbers 227 kB 2238 September 3, 2019
Divisibility of positive improper fractions 248.8 kB 2226 September 3, 2019
Non positive
Divisibility of integers 143.7 kB 2644 September 3, 2019
Divisibility of decimals 222.3 kB 2411 September 3, 2019
Divisibility of fractions 260.9 kB 2432 September 3, 2019
Divisibility of mixed numbers 276.9 kB 2076 September 3, 2019
Divisibility of improper fractions 234.4 kB 2037 September 3, 2019
Factoring numbers
Factoring 198.2 kB 3744 September 3, 2019