# How to Find Factors of Numbers?

A factor of a number in mathematics is a number that divides the given number. In this step-by-step guide, you learn more about finding factors of numbers.

A factor is a Latin word, meaning “a doer” or “a maker” or “a performer.” We can use the multiplication as well as the division method, to find the factors.

## Related Topics

## A step-by-step guide to factoring numbers

In mathematics, a factor is a number that divides another number evenly, that is without remainder. The factors of a number can be called numbers or algebraic expressions that evenly divide a given number/expression. The factors of a number can either be positive or negative.

### Properties of factors

Factors of a number have several properties. The following are the properties of the 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 operations used to find factors.

### How to find factors of a number?

We can use “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.

**Factors by multiplication**

To find the factors using the multiplication:

- Write the given number as the product of two numbers in different possible ways.
- All the numbers that are involved in all these products are the factors of the given number.

### How to find the number of factors?

Using the following steps we can find the number of factors of a given number.

**Step 1:**Find its prime factorization, that is, express it as the product of primes.**Step 2:**Write the prime factorization in the exponent form.**Step 3:**Add \(1\) to each of the exponents.**Step 4:**Multiply all the resultant numbers. This product would give the number of factors of the given number.

## Exercises for Factoring Numbers

### Find the positive factors of each number.

- \(\color{blue}{80}\)
- \(\color{blue}{132}\)
- \(\color{blue}{270}\)
- \(\color{blue}{450}\)

- \(\color{blue}{1,2,4,5,8,10,16,20,40,80}\)
- \(\color{blue}{1,2,3,4,6,11,12,22,33,44,66,132}\)
- \(\color{blue}{1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270}\)
- \(\color{blue}{1,2,3,5,6,9,10,15,18,25,30,45,50,75,90,150,225,450}\)

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