Factors calculator with steps

Factors calculator

What is a Factor?

A factor of a number is a number that divides it without producing a remainder. It divides a number evenly without resulting into fractions, decimals, or any other form of remainder. Therefore, it’s a full divisor of the given number. You can find the factors by applying multiplication or division rules. Furthermore. You can find the factors of a number by using factoring skills. Factors can also be algebraic expressions that divide other expressions or a given number without remainders. A factor can either be a negative or positive number or expression.

Types of Factors

Prime Factor

A prime factor refers to a number that only has two factors, that is, 1 and the number itself. Therefore a prime factor is a factor that is a prime number. In simple terms, it is a number greater than 1 that cannot be divided by other numbers rather than 1 and the number itself.

Highest Common Factor (HCF)

Highest Common Factor of two or more numbers refers to the greatest factors that can divide both numbers evenly. For example, the HCF of 15 and 30 is 15. This is because 15 can divide 15 once and 30 two times.

Common Factor

These are overlapping numbers that are also factors of two or more numbers hence the name common factors. An example is 1, 2, 3. These numbers are common factors for 12, 18, 24, and so on.

How to find Factors?

There are two main ways to find the division of a number. By using Long division and Multiplication

Division Method

For the division method, you need to divide every number less than or equal to the given numbers then and pick only the ones with 0 as a remainder.

For example, 1, 2, 4 and 8 are divisors of 4 because the remainder is 0

Steps for finding Factors using the division method

  •    List all the numbers that are equal to or less than the given number
  •  Divide the provided number by each of the numbers that you have listed
  •    Pick only the numbers that result in 0 as a remainder

Multiplication Method

You can find the factors of a number by multiplying 2 pairs of numbers that will result in the given number.

For example; the factors of 16 are all the following pairs multiplied together

1 × 16 = 16

2 × 8 = 16

4 × 4 = 16

Factors of 16 are

1, 2, 4, 8 and 16

Applications of Factors

Equal Division- Factoring can be applied in real life when it comes to sharing items. A good Example is 3 People sharing a pizza. They can divide it into twelve pieces so that each gets 4 pieces.

Money- Factoring is an important measure to divide money into equal units. For Example, you can divide One dollar into 4 four quarters.

Solving Algebraic Expressions- The algebraic expressions depend heavily on factoring.


Factors video tutorial

Solved Factors Examples

Factors of 2

Factors of 12

Factors of 23

Factors of 44

Factors of 56

Factors of 102

Factors Facts

  •        Factors cannot be fractions or decimals but whole numbers
  •       5 is a factor for every number that ends with a 5 or a 0
  •      2 is a factor for every even number
  •     2, 5, and 10 are factors for every number greater than 0 that ends with a 0
  •     Algebraic expressions can be simplified by the factoring method
  •    There are finite factors of a number
  •   All numbers except 1 and 0 have two factors which are 1 and the number itself.
  •   A factor must be less or equal to the given number

Factors Frequently Asked Questions

1. What is the difference between a divisor and a Factor?

A divisor is a number that divides another number regardless of whether it produces a remainder or not. Contrary, a factor is a number that divides another number and produces no or 0 as the remainder.

2. What is the difference between factors and Prime Factors?

Factors are numbers that divide another number without a remainder. On the other hand, rime factors are factors greater than 1 that are prime numbers. That means they can only be divided by one and the number itself.