How to Find the Factors of a Number

How to Find the Factors of a Number?

Mathematics is all about numbers and the study of their types, properties, and concepts. Factors are key concepts taught in arithmetic at the elementary stage. A factor is a number that gives no remainder after it is divided by a specific number. Factors of a number are terminable.

How to Find the Factors of a Number?

Factoring is a useful skill to find factors, which is further utilized, in real-life situations, such as dividing something into equal parts or dividing into rows and columns, comparing prices, exchanging money and understanding time, and making calculations, during travel.

What are Factors?

The term ‘factors’ is derived from a Latin word that means a maker. A factor represents the numbers that divide the given number absolutely, without leaving any remainder. For example, 4 is the factor of 12 since on dividing 12 by 4, we get 3, and it does not leave any remainder. The other factors of 12 are 1, 2, 3, and 6. Moreover, factors are the numbers one can multiply with each other to obtain the required number. Every number has a minimum of two factors, i.e., one and the number itself.

To determine the factors of a given number, you need to identify the numbers that evenly divide that particular number. In order to do so, start with dividing by number one, as one is the factor of every number.

How to Find Factors of a Number?

We can use both “Division” and “Multiplication” to find the factors.

Factors by Division

To find the factors of a number using division:

  • Find all the numbers less than or equal to the given number.
  • Divide the given number by each of the numbers.
  • The divisors that give the remainder to be 0 are the factors of the number

Dividing by Prime Numbers

The easiest way to find the factors of a large number is to divide it by the smallest prime number greater than 1 which divides it evenly without any remainder. Keep performing this division process with each number, until you get 1.

Apply Divisibility Rules

Memorizing some divisibility rules will be helpful in finding the factors of a number. For example, if a number is even, it’s divisible by 2, i.e. 2 is a factor. If a number’s digits total a number that’s divisible by 3, the number itself is divisible by 3, i.e. 3 is a factor. If a number ends with a 0 or a 5, it’s divisible by 5, i.e. 5 is a factor.

If a number is divisible twice by 2, it’s divisible by 4, i.e. 4 is a factor. If a number is divisible by 2 and by 3, it’s divisible by 6, i.e. 6 is a factor. If a number is divisible twice by 3 (or if the sum of the digits is divisible by 9), then it’s divisible by 9, i.e. 9 is a factor.

Properties of Factors

Factors of a number have a certain number of properties. Given below are the properties of factors:

  • The number of factors of a number is finite.
  • A factor of a number is always less than or equal to the given number.
  • Every number except 0 and 1 has at least two factors, 1 and itself.
  • Division and multiplication are the operations that are used in finding the factors.

Factors & Common Factors:

Factors of any number are the numbers that, on multiplying, produce back the number. Common factors of any two given numbers are the numbers that divide those numbers completely.


Finding factors is a crucial math skill required for understanding other math topics. When children learn math through reasoning and logic, they gain conceptual fluency in various complex topics. Cuemath online math classes help kids to understand math logically by strengthening their reasoning skills. Sound conceptual knowledge of each topic allows children to develop connections between various math topics, forming a strong math foundation.

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