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 4815 September 3, 2019
Divisibility of positive integers – easy 157.4 kB 3437 September 3, 2019
Divisibility of positive integers – medium 164.8 kB 4147 September 3, 2019
Divisibility of positive integers – hard 179.1 kB 3356 September 3, 2019
Positive decimals
Divisibility of positive decimals – very easy 559.2 kB 1702 September 3, 2019
Divisibility of positive decimals – easy 572.4 kB 1665 September 3, 2019
Divisibility of positive decimals – medium 575.7 kB 1601 September 3, 2019
Divisibility of positive decimals – hard 561.3 kB 1609 September 3, 2019
Positive fractions
Divisibility of positive fractions – very easy 119 kB 1661 September 3, 2019
Divisibility of positive fractions – easy 564.6 kB 1493 September 3, 2019
Divisibility of positive fractions – medium 572.1 kB 1671 September 3, 2019
Divisibility of positive fractions – hard 576.9 kB 1425 September 3, 2019
Positive mixed numbers
Divisibility of positive mixed numbers – easy 568.8 kB 1528 September 3, 2019
Divisibility of positive mixed numbers – medium 583.9 kB 1384 September 3, 2019
Divisibility of positive mixed numbers – hard 612.3 kB 1318 September 3, 2019
Positive improper fractions
Divisibility of positive improper fractions – very easy 170.5 kB 1385 September 3, 2019
Divisibility of positive improper fractions – easy 564.5 kB 1303 September 3, 2019
Divisibility of positive improper fractions – medium 564.4 kB 1260 September 3, 2019
Divisibility of positive improper fractions – hard 574.6 kB 1361 September 3, 2019
Divisibility of positive improper fractions – very hard 574.1 kB 1262 September 3, 2019
Non positive integers
Divisibility of integers – very easy 82.3 kB 1559 September 3, 2019
Divisibility of integers – easy 154.6 kB 1547 September 3, 2019
Divisibility of integers – medium 163.2 kB 1821 September 3, 2019
Divisibility of integers – hard 173.4 kB 1919 September 3, 2019
Non positive decimals
Divisibility of decimals – very easy 567.8 kB 1390 September 3, 2019
Divisibility of decimals – easy 559.9 kB 1550 September 3, 2019
Divisibility of decimals – medium 557 kB 1325 September 3, 2019
Divisibility of decimals – hard 559.6 kB 1651 September 3, 2019
Non positive fractions
Divisibility of fractions – very easy 552.2 kB 1382 September 3, 2019
Divisibility of fractions – easy 569.2 kB 1453 September 3, 2019
Divisibility of fractions – medium 571.5 kB 1345 September 3, 2019
Divisibility of fractions – hard 595.4 kB 1431 September 3, 2019
Non positive mixed numbers
Divisibility of mixed numbers – easy 559.7 kB 1416 September 3, 2019
Divisibility of mixed numbers – medium 588.7 kB 1366 September 3, 2019
Divisibility of mixed numbers – hard 585.2 kB 1312 September 3, 2019
Non positive improper fractions
Divisibility of improper fractions – easy 175 kB 1600 September 3, 2019
Divisibility of improper fractions – medium 183.4 kB 1497 September 3, 2019
Divisibility of improper fractions – hard 212.8 kB 1670 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 2879 September 3, 2019
Factoring numbers without exponents 125.7 kB 1985 September 3, 2019
Factoring with exponents 129.8 kB 2468 September 3, 2019

Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 137.7 kB 2328 September 3, 2019
Divisibility of positive decimals 192.9 kB 1518 September 3, 2019
Divisibility of positive fractions 252.6 kB 1355 September 3, 2019
Divisibility of positive mixed numbers 227 kB 1281 September 3, 2019
Divisibility of positive improper fractions 248.8 kB 1322 September 3, 2019
Non positive
Divisibility of integers 143.7 kB 1595 September 3, 2019
Divisibility of decimals 222.3 kB 1388 September 3, 2019
Divisibility of fractions 260.9 kB 1437 September 3, 2019
Divisibility of mixed numbers 276.9 kB 1270 September 3, 2019
Divisibility of improper fractions 234.4 kB 1310 September 3, 2019
Factoring numbers
Factoring 198.2 kB 2681 September 3, 2019