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 3319 October 13, 2012
Divisibility of positive integers – easy 157.4 kB 2350 October 13, 2012
Divisibility of positive integers – medium 164.8 kB 3014 October 13, 2012
Divisibility of positive integers – hard 179.1 kB 2284 October 13, 2012
Positive decimals
Divisibility of positive decimals – very easy 559.2 kB 1001 October 13, 2012
Divisibility of positive decimals – easy 572.4 kB 966 October 13, 2012
Divisibility of positive decimals – medium 575.7 kB 960 October 13, 2012
Divisibility of positive decimals – hard 561.3 kB 957 October 13, 2012
Positive fractions
Divisibility of positive fractions – very easy 119 kB 997 October 13, 2012
Divisibility of positive fractions – easy 564.6 kB 881 October 13, 2012
Divisibility of positive fractions – medium 572.1 kB 938 October 13, 2012
Divisibility of positive fractions – hard 576.9 kB 814 October 13, 2012
Positive mixed numbers
Divisibility of positive mixed numbers – easy 568.8 kB 930 October 13, 2012
Divisibility of positive mixed numbers – medium 583.9 kB 810 October 13, 2012
Divisibility of positive mixed numbers – hard 612.3 kB 828 October 13, 2012
Positive improper fractions
Divisibility of positive improper fractions – very easy 170.5 kB 820 October 13, 2012
Divisibility of positive improper fractions – easy 564.5 kB 801 October 13, 2012
Divisibility of positive improper fractions – medium 564.4 kB 764 October 13, 2012
Divisibility of positive improper fractions – hard 574.6 kB 816 October 13, 2012
Divisibility of positive improper fractions – very hard 574.1 kB 776 October 13, 2012
Non positive integers
Divisibility of integers – very easy 82.3 kB 899 October 13, 2012
Divisibility of integers – easy 154.6 kB 990 October 13, 2012
Divisibility of integers – medium 163.2 kB 1203 October 13, 2012
Divisibility of integers – hard 173.4 kB 1224 October 13, 2012
Non positive decimals
Divisibility of decimals – very easy 567.8 kB 872 October 13, 2012
Divisibility of decimals – easy 559.9 kB 923 October 13, 2012
Divisibility of decimals – medium 557 kB 839 October 13, 2012
Divisibility of decimals – hard 559.6 kB 1035 October 13, 2012
Non positive fractions
Divisibility of fractions – very easy 552.2 kB 857 October 13, 2012
Divisibility of fractions – easy 569.2 kB 859 October 13, 2012
Divisibility of fractions – medium 571.5 kB 809 October 13, 2012
Divisibility of fractions – hard 595.4 kB 839 October 13, 2012
Non positive mixed numbers
Divisibility of mixed numbers – easy 559.7 kB 819 October 13, 2012
Divisibility of mixed numbers – medium 588.7 kB 819 October 13, 2012
Divisibility of mixed numbers – hard 585.2 kB 776 October 13, 2012
Non positive improper fractions
Divisibility of improper fractions – easy 175 kB 980 October 13, 2012
Divisibility of improper fractions – medium 183.4 kB 897 October 13, 2012
Divisibility of improper fractions – hard 212.8 kB 1125 October 13, 2012

 

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 1942 October 13, 2012
Factoring numbers without exponents 125.7 kB 1206 October 13, 2012
Factoring with exponents 129.8 kB 1429 October 13, 2012


Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 137.7 kB 1524 October 14, 2012
Divisibility of positive decimals 192.9 kB 963 October 14, 2012
Divisibility of positive fractions 252.6 kB 835 October 14, 2012
Divisibility of positive mixed numbers 227 kB 793 October 14, 2012
Divisibility of positive improper fractions 248.8 kB 830 October 14, 2012
Non positive
Divisibility of integers 143.7 kB 986 October 14, 2012
Divisibility of decimals 222.3 kB 867 October 14, 2012
Divisibility of fractions 260.9 kB 916 October 14, 2012
Divisibility of mixed numbers 276.9 kB 820 October 14, 2012
Divisibility of improper fractions 234.4 kB 834 October 14, 2012
Factoring numbers
Factoring 198.2 kB 1549 October 14, 2012


Divisibility knowledge test