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 4621 September 3, 2019
Divisibility of positive integers – easy 157.4 kB 3303 September 3, 2019
Divisibility of positive integers – medium 164.8 kB 3963 September 3, 2019
Divisibility of positive integers – hard 179.1 kB 3110 September 3, 2019
Positive decimals
Divisibility of positive decimals – very easy 559.2 kB 1595 September 3, 2019
Divisibility of positive decimals – easy 572.4 kB 1540 September 3, 2019
Divisibility of positive decimals – medium 575.7 kB 1487 September 3, 2019
Divisibility of positive decimals – hard 561.3 kB 1501 September 3, 2019
Positive fractions
Divisibility of positive fractions – very easy 119 kB 1539 September 3, 2019
Divisibility of positive fractions – easy 564.6 kB 1399 September 3, 2019
Divisibility of positive fractions – medium 572.1 kB 1530 September 3, 2019
Divisibility of positive fractions – hard 576.9 kB 1302 September 3, 2019
Positive mixed numbers
Divisibility of positive mixed numbers – easy 568.8 kB 1419 September 3, 2019
Divisibility of positive mixed numbers – medium 583.9 kB 1276 September 3, 2019
Divisibility of positive mixed numbers – hard 612.3 kB 1235 September 3, 2019
Positive improper fractions
Divisibility of positive improper fractions – very easy 170.5 kB 1277 September 3, 2019
Divisibility of positive improper fractions – easy 564.5 kB 1195 September 3, 2019
Divisibility of positive improper fractions – medium 564.4 kB 1154 September 3, 2019
Divisibility of positive improper fractions – hard 574.6 kB 1277 September 3, 2019
Divisibility of positive improper fractions – very hard 574.1 kB 1166 September 3, 2019
Non positive integers
Divisibility of integers – very easy 82.3 kB 1455 September 3, 2019
Divisibility of integers – easy 154.6 kB 1459 September 3, 2019
Divisibility of integers – medium 163.2 kB 1703 September 3, 2019
Divisibility of integers – hard 173.4 kB 1797 September 3, 2019
Non positive decimals
Divisibility of decimals – very easy 567.8 kB 1304 September 3, 2019
Divisibility of decimals – easy 559.9 kB 1440 September 3, 2019
Divisibility of decimals – medium 557 kB 1246 September 3, 2019
Divisibility of decimals – hard 559.6 kB 1543 September 3, 2019
Non positive fractions
Divisibility of fractions – very easy 552.2 kB 1274 September 3, 2019
Divisibility of fractions – easy 569.2 kB 1345 September 3, 2019
Divisibility of fractions – medium 571.5 kB 1237 September 3, 2019
Divisibility of fractions – hard 595.4 kB 1322 September 3, 2019
Non positive mixed numbers
Divisibility of mixed numbers – easy 559.7 kB 1311 September 3, 2019
Divisibility of mixed numbers – medium 588.7 kB 1282 September 3, 2019
Divisibility of mixed numbers – hard 585.2 kB 1202 September 3, 2019
Non positive improper fractions
Divisibility of improper fractions – easy 175 kB 1508 September 3, 2019
Divisibility of improper fractions – medium 183.4 kB 1393 September 3, 2019
Divisibility of improper fractions – hard 212.8 kB 1566 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 2752 September 3, 2019
Factoring numbers without exponents 125.7 kB 1743 September 3, 2019
Factoring with exponents 129.8 kB 2381 September 3, 2019

Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 137.7 kB 2188 September 3, 2019
Divisibility of positive decimals 192.9 kB 1443 September 3, 2019
Divisibility of positive fractions 252.6 kB 1248 September 3, 2019
Divisibility of positive mixed numbers 227 kB 1181 September 3, 2019
Divisibility of positive improper fractions 248.8 kB 1235 September 3, 2019
Non positive
Divisibility of integers 143.7 kB 1489 September 3, 2019
Divisibility of decimals 222.3 kB 1302 September 3, 2019
Divisibility of fractions 260.9 kB 1326 September 3, 2019
Divisibility of mixed numbers 276.9 kB 1198 September 3, 2019
Divisibility of improper fractions 234.4 kB 1254 September 3, 2019
Factoring numbers
Factoring 198.2 kB 2524 September 3, 2019