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 3727 October 13, 2012
Divisibility of positive integers – easy 157.4 kB 2624 October 13, 2012
Divisibility of positive integers – medium 164.8 kB 3333 October 13, 2012
Divisibility of positive integers – hard 179.1 kB 2563 October 13, 2012
Positive decimals
Divisibility of positive decimals – very easy 559.2 kB 1195 October 13, 2012
Divisibility of positive decimals – easy 572.4 kB 1073 October 13, 2012
Divisibility of positive decimals – medium 575.7 kB 1097 October 13, 2012
Divisibility of positive decimals – hard 561.3 kB 1124 October 13, 2012
Positive fractions
Divisibility of positive fractions – very easy 119 kB 1177 October 13, 2012
Divisibility of positive fractions – easy 564.6 kB 1030 October 13, 2012
Divisibility of positive fractions – medium 572.1 kB 1131 October 13, 2012
Divisibility of positive fractions – hard 576.9 kB 956 October 13, 2012
Positive mixed numbers
Divisibility of positive mixed numbers – easy 568.8 kB 1087 October 13, 2012
Divisibility of positive mixed numbers – medium 583.9 kB 909 October 13, 2012
Divisibility of positive mixed numbers – hard 612.3 kB 915 October 13, 2012
Positive improper fractions
Divisibility of positive improper fractions – very easy 170.5 kB 941 October 13, 2012
Divisibility of positive improper fractions – easy 564.5 kB 900 October 13, 2012
Divisibility of positive improper fractions – medium 564.4 kB 857 October 13, 2012
Divisibility of positive improper fractions – hard 574.6 kB 944 October 13, 2012
Divisibility of positive improper fractions – very hard 574.1 kB 847 October 13, 2012
Non positive integers
Divisibility of integers – very easy 82.3 kB 1064 October 13, 2012
Divisibility of integers – easy 154.6 kB 1110 October 13, 2012
Divisibility of integers – medium 163.2 kB 1359 October 13, 2012
Divisibility of integers – hard 173.4 kB 1421 October 13, 2012
Non positive decimals
Divisibility of decimals – very easy 567.8 kB 962 October 13, 2012
Divisibility of decimals – easy 559.9 kB 1075 October 13, 2012
Divisibility of decimals – medium 557 kB 927 October 13, 2012
Divisibility of decimals – hard 559.6 kB 1220 October 13, 2012
Non positive fractions
Divisibility of fractions – very easy 552.2 kB 960 October 13, 2012
Divisibility of fractions – easy 569.2 kB 998 October 13, 2012
Divisibility of fractions – medium 571.5 kB 910 October 13, 2012
Divisibility of fractions – hard 595.4 kB 993 October 13, 2012
Non positive mixed numbers
Divisibility of mixed numbers – easy 559.7 kB 974 October 13, 2012
Divisibility of mixed numbers – medium 588.7 kB 952 October 13, 2012
Divisibility of mixed numbers – hard 585.2 kB 857 October 13, 2012
Non positive improper fractions
Divisibility of improper fractions – easy 175 kB 1160 October 13, 2012
Divisibility of improper fractions – medium 183.4 kB 1052 October 13, 2012
Divisibility of improper fractions – hard 212.8 kB 1250 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 2184 October 13, 2012
Factoring numbers without exponents 125.7 kB 1320 October 13, 2012
Factoring with exponents 129.8 kB 1731 October 13, 2012


Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 137.7 kB 1747 October 14, 2012
Divisibility of positive decimals 192.9 kB 1106 October 14, 2012
Divisibility of positive fractions 252.6 kB 931 October 14, 2012
Divisibility of positive mixed numbers 227 kB 884 October 14, 2012
Divisibility of positive improper fractions 248.8 kB 958 October 14, 2012
Non positive
Divisibility of integers 143.7 kB 1172 October 14, 2012
Divisibility of decimals 222.3 kB 959 October 14, 2012
Divisibility of fractions 260.9 kB 1037 October 14, 2012
Divisibility of mixed numbers 276.9 kB 902 October 14, 2012
Divisibility of improper fractions 234.4 kB 995 October 14, 2012
Factoring numbers
Factoring 198.2 kB 1799 October 14, 2012


Divisibility knowledge test