Easily calculate the factors of any number on Examples.com. Input the number to quickly find all its factors, including prime and composite factors, perfect for math and educational purposes.

A factor is a number that divides another number exactly, leaving no remainder. Factors are essential in mathematics for simplifying expressions, solving equations, and understanding number properties. Every number has at least two factors: 1 and the number itself. Some numbers, known as prime numbers, have only these two factors, while composite numbers have additional factors. Finding factors helps in tasks such as factoring algebraic expressions, calculating the greatest common factor (GCF), and simplifying fractions. Understanding factors is crucial for many areas of math, including number theory, algebra, and geometry.

## How to Find the Factor

### Step 1: Input the Number

Enter the number you want to factor into the **“Number”** input field.

### Step 2: Calculate the Factors

Click on the **“Calculate”** button to process the factors for the entered number.

### Step 3: View the Results

Once you click calculate, the tool will display the factors of the number.

### Step 4: Explore Factor Pairs

Click on the **“Factor Pairs”** button to view pairs of numbers that multiply to give the original number.

### Step 5: Find Prime Factors

Click on the **“Prime Factors”** button to view the prime factors of the number.

## Properties of Factors

**Divisibility**: A factor is a number that divides another number exactly without leaving a remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4 with no remainder.**Non-Negative**: Factors of a number are always positive integers, although negative factors can also be used in certain mathematical contexts.**Finite Set**: Every whole number has a finite number of factors. For example, the number 12 has six factors: 1, 2, 3, 4, 6, and 12.**Factor Pairs**: Factors always come in pairs. For example, for 12, the pairs are (1,12), (2,6), and (3,4). These pairs multiply to give the original number.**1 is a Universal Factor**: The number 1 is a factor of every integer, as any number divided by 1 results in the same number.**The Number Itself is a Factor**: Any number is a factor of itself because it divides evenly into itself. For example, 7 is a factor of 7.**Prime Factors**: Prime factors are factors that are prime numbers. Any number can be expressed as a product of prime factors. For example, the prime factors of 12 are 2 and 3.**Common Factors**: If two or more numbers share the same factor, it is called a common factor. For example, the numbers 12 and 18 share the factors 1, 2, 3, and 6.**Greatest Common Factor (GCF)**: The largest factor common to two or more numbers is called the greatest common factor. For example, the GCF of 12 and 18 is 6.**Zero and Negative Numbers**: Zero does not have factors because no number multiplied by another can result in zero. Similarly, factors of negative numbers are the negative counterparts of the positive factors.

## Factors of Prime and Composite Numbers

Prime Numbers | Composite Numbers |
---|---|

Prime numbers have only 2 factors: 1 and the number itself. | Composite numbers have more than 2 factors. |

Examples: | Examples: |

2: Factors are 1, 2 | 12: Factors are 1, 2, 3, 4, 6, 12 |

3: Factors are 1, 3 | 18: Factors are 1, 2, 3, 6, 9, 18 |

5: Factors are 1, 5 | 20: Factors are 1, 2, 4, 5, 10, 20 |

7: Factors are 1, 7 | 28: Factors are 1, 2, 4, 7, 14, 28 |

11: Factors are 1, 11 | 36: Factors are 1, 2, 3, 4, 6, 9, 12, 18, 36 |

## Finding Factors using Multiplication and Division

### 1. Using Multiplication:

**Multiplication** method finds factors by identifying factor pairs that multiply to the original number.

To find factors through multiplication, we look for all pairs of numbers that multiply to give the original number. These pairs are called factor pairs.

#### Example:

For the number **24**, find the multiplication pairs:

- 1 × 24 = 24
- 2 × 12 = 24
- 3 × 8 = 24
- 4 × 6 = 24

So, the factors of 24 are **1, 2, 3, 4, 6, 8, 12, 24**.

### 2. Using Division:

**Division** method identifies factors by dividing the number and checking for whole numbers without remainders.

To find factors through division, divide the original number by integers starting from 1. If the division results in a whole number with no remainder, both the divisor and quotient are factors.

#### Example:

For the number **36**, use division:

- 36 ÷ 1 = 36 (Factors: 1, 36)
- 36 ÷ 2 = 18 (Factors: 2, 18)
- 36 ÷ 3 = 12 (Factors: 3, 12)
- 36 ÷ 4 = 9 (Factors: 4, 9)
- 36 ÷ 6 = 6 (Factors: 6, 6)

So, the factors of 36 are **1, 2, 3, 4, 6, 9, 12, 18, 36**.

## Examples of Factors

### Example 1: Factors of 12

To find the factors of 12:

- 12 ÷ 1 = 12 → (1, 12)
- 12 ÷ 2 = 6 → (2, 6)
- 12 ÷ 3 = 4 → (3, 4) So, the factors of 12 are
**1, 2, 3, 4, 6, 12**.

### Example 2: Factors of 18

To find the factors of 18:

- 18 ÷ 1 = 18 → (1, 18)
- 18 ÷ 2 = 9 → (2, 9)
- 18 ÷ 3 = 6 → (3, 6) So, the factors of 18 are
**1, 2, 3, 6, 9, 18**.

### Example 3: Factors of 28

To find the factors of 28:

- 28 ÷ 1 = 28 → (1, 28)
- 28 ÷ 2 = 14 → (2, 14)
- 28 ÷ 4 = 7 → (4, 7) So, the factors of 28 are
**1, 2, 4, 7, 14, 28**.

### Example 4: Factors of 36

To find the factors of 36:

- 36 ÷ 1 = 36 → (1, 36)
- 36 ÷ 2 = 18 → (2, 18)
- 36 ÷ 3 = 12 → (3, 12)
- 36 ÷ 4 = 9 → (4, 9)
- 36 ÷ 6 = 6 → (6, 6) So, the factors of 36 are
**1, 2, 3, 4, 6, 9, 12, 18, 36**.

### Example 5: Factors of 50

To find the factors of 50:

- 50 ÷ 1 = 50 → (1, 50)
- 50 ÷ 2 = 25 → (2, 25)
- 50 ÷ 5 = 10 → (5, 10) So, the factors of 50 are
**1, 2, 5, 10, 25, 50**.

## How do I find the factors of a number?

To find factors, divide the number by integers starting from 1. If the division leaves no remainder, both the divisor and quotient are factors.

## What are factor pairs?

Factor pairs are two numbers that multiply together to give the original number. For example, the factor pairs of 24 are (1, 24), (2, 12), (3, 8), and (4, 6).

## Can factors be negative?

Yes, factors can be negative. For example, the factors of 12 are ±1, ±2, ±3, ±4, ±6, and ±12, since both positive and negative numbers can divide the original number without leaving a remainder.

## Do all numbers have a finite number of factors?

Yes, every whole number has a finite number of factors. For example, 24 has eight factors: 1, 2, 3, 4, 6, 8, 12, and 24.

## Can a number have only one factor?

Yes, 1 is the only number that has exactly one factor, which is 1 itself. Every other number has at least two factors.

## Can a prime number be a composite number?

No, prime numbers and composite numbers are mutually exclusive. A prime number has exactly two factors (1 and itself), while a composite number has more than two factors.