**Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36**

**Prime Factorization of 36: 2 × 2 × 3 × 3 or 2**^{2}** × 3**^{2}

In Maths, a divisor of any integer n, also called a factor of n, is an integer m that may be multiplied by some integer to generate n. We can also say n is a multiple of m. A factor is a number that divides the original number directly or evenly. A factor is a number that can divide a greater number evenly.

## What are the Factors?

A factor is a number that can divide a greater number evenly with no remainder called a factor.

## Properties of Factors

The factors of a number have the following properties:

- The number of Factors is finite
- The factor of a number is less or equal to the given number
- Every number has at least two factors 1 and the number itself except 0 and 1
- We can find any number factor with the help of Division and multiplication operation

## How to Find Factors of a Number?

To find the factor of any number, we use the division method and the multiplication method

### Finding Factors using Division Method

Firstly we find the factor of any number with the division method.

Example Find the Factor of 36 with the division method.

Solution –

**Step 1: **Divide 36 with 2

36 ÷ 2 = 18

**Step 2: **Again divide 18 with 2

18 ÷ 2 = 9

**Step 3: **Since 9 is no more divisible by 2, move to the next prime number i.e. 3

9 ÷ 3 = 3

**Step 4: **Finally, divide 3 with 3 to get 1.

3 ÷ 3 = 1

- First, we have to check the total number divided 36. We check it from 1 to 9 and note that the numbers divide 36 completely.
- The number which completely divides 36 without leaving a remainder is called the factor of 36. We have to note that number and make a list of its pair. All number is upto 9; We automatically get the other pair factor along with it.

For example, we have to write like

36÷1 = 36

36÷2 = 18

36÷3 = 12

36÷4 = 9

So on…

- After this list, we have all the factors of 36 starting from 1 and up there, coming down, and we go up again up to 36, it will provide a complete list of all factors of 36

### Finding Factors using Multiplication Method

To find the factor of 36 we have to follow the same method we listed above with some additional changes.

**Example:** Find the factors of 36 using the multiplication method.

**Step 1 – **We must check what pair of numbers multiply to give us 36, so we divide 36 by numbers from 1 to 9.

**Step 2 – **We make a list of this number with its pair. From it, we automatically get another pair of factors.

1 × 36 = 36

2 × 36 = 72

So on

**Step 3 – **After all lists, we have the factor of 36 from 1 to up there, coming down and then going up again to 36

The Positive factor of 36 is – 1, 2, 3, 4, 6, 9, 12, 18, and 36

## Factors of 36 in Pairs

The factors of 36 can be written in pairs.

Factors |
Positive Pair Factors |

1 × 36 = 36 | 1, 36 |

2 × 18 = 36 | 2, 18 |

3 × 12 = 36 | 3, 12 |

4 × 9 = 36 | 4, 9 |

6 × 6 = 36 | 6, 6 |

The Negative Factor of 36 – 1, -2, -3, -4, -6, -9, -12, -18, and -36

Factors |
Negative Pair Factors |

-1 × -36 = 36 | -1, -36 |

-2 × -18 = 36 | -2, -18 |

-3 × -12 = 36 | -3, -12 |

-4 × -9 = 36 | -4, -9 |

-6 × -6 = 36 | -6, -6 |

### FAQ

**What is 36 ka prime factor?**

2 & 3

**What are factors 36?**

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

**What is the prime factorization of 36?**

The prime factorization of 36 is 2 × 2 × 3 × 3 or 22 × 32.

**What are the positive pair factors of 36?**

The positive pair factors of 36 are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6).

**Write down the negative pair factors of 36?**

The negative pair factors of 36 are (-1, -36), (-2, -18), (-3, -12), (-4, -9), and (-6, -6).

**Which is not a factor of 36?**

Therefore, 6 and 5 is not factor pair of 36.

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