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 4665 September 3, 2019
Divisibility of positive integers – easy 157.4 kB 3335 September 3, 2019
Divisibility of positive integers – medium 164.8 kB 3993 September 3, 2019
Divisibility of positive integers – hard 179.1 kB 3169 September 3, 2019
Positive decimals
Divisibility of positive decimals – very easy 559.2 kB 1622 September 3, 2019
Divisibility of positive decimals – easy 572.4 kB 1565 September 3, 2019
Divisibility of positive decimals – medium 575.7 kB 1510 September 3, 2019
Divisibility of positive decimals – hard 561.3 kB 1522 September 3, 2019
Positive fractions
Divisibility of positive fractions – very easy 119 kB 1563 September 3, 2019
Divisibility of positive fractions – easy 564.6 kB 1427 September 3, 2019
Divisibility of positive fractions – medium 572.1 kB 1555 September 3, 2019
Divisibility of positive fractions – hard 576.9 kB 1323 September 3, 2019
Positive mixed numbers
Divisibility of positive mixed numbers – easy 568.8 kB 1438 September 3, 2019
Divisibility of positive mixed numbers – medium 583.9 kB 1293 September 3, 2019
Divisibility of positive mixed numbers – hard 612.3 kB 1257 September 3, 2019
Positive improper fractions
Divisibility of positive improper fractions – very easy 170.5 kB 1295 September 3, 2019
Divisibility of positive improper fractions – easy 564.5 kB 1217 September 3, 2019
Divisibility of positive improper fractions – medium 564.4 kB 1171 September 3, 2019
Divisibility of positive improper fractions – hard 574.6 kB 1299 September 3, 2019
Divisibility of positive improper fractions – very hard 574.1 kB 1182 September 3, 2019
Non positive integers
Divisibility of integers – very easy 82.3 kB 1475 September 3, 2019
Divisibility of integers – easy 154.6 kB 1483 September 3, 2019
Divisibility of integers – medium 163.2 kB 1727 September 3, 2019
Divisibility of integers – hard 173.4 kB 1822 September 3, 2019
Non positive decimals
Divisibility of decimals – very easy 567.8 kB 1327 September 3, 2019
Divisibility of decimals – easy 559.9 kB 1462 September 3, 2019
Divisibility of decimals – medium 557 kB 1268 September 3, 2019
Divisibility of decimals – hard 559.6 kB 1562 September 3, 2019
Non positive fractions
Divisibility of fractions – very easy 552.2 kB 1296 September 3, 2019
Divisibility of fractions – easy 569.2 kB 1363 September 3, 2019
Divisibility of fractions – medium 571.5 kB 1257 September 3, 2019
Divisibility of fractions – hard 595.4 kB 1346 September 3, 2019
Non positive mixed numbers
Divisibility of mixed numbers – easy 559.7 kB 1335 September 3, 2019
Divisibility of mixed numbers – medium 588.7 kB 1304 September 3, 2019
Divisibility of mixed numbers – hard 585.2 kB 1222 September 3, 2019
Non positive improper fractions
Divisibility of improper fractions – easy 175 kB 1537 September 3, 2019
Divisibility of improper fractions – medium 183.4 kB 1413 September 3, 2019
Divisibility of improper fractions – hard 212.8 kB 1588 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 2777 September 3, 2019
Factoring numbers without exponents 125.7 kB 1800 September 3, 2019
Factoring with exponents 129.8 kB 2411 September 3, 2019

Divisibility and factoring worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Divisibility of positive integers 137.7 kB 2216 September 3, 2019
Divisibility of positive decimals 192.9 kB 1460 September 3, 2019
Divisibility of positive fractions 252.6 kB 1270 September 3, 2019
Divisibility of positive mixed numbers 227 kB 1206 September 3, 2019
Divisibility of positive improper fractions 248.8 kB 1254 September 3, 2019
Non positive
Divisibility of integers 143.7 kB 1509 September 3, 2019
Divisibility of decimals 222.3 kB 1325 September 3, 2019
Divisibility of fractions 260.9 kB 1346 September 3, 2019
Divisibility of mixed numbers 276.9 kB 1218 September 3, 2019
Divisibility of improper fractions 234.4 kB 1268 September 3, 2019
Factoring numbers
Factoring 198.2 kB 2561 September 3, 2019