If a number completely divides 36 without leaving a remainder, then that number is called a factor of 36. Thus we can say that the factors of 36 are the divisors of 36. In this section, we will learn about the factors of 36 and the prime factors of 36.

**Also Read: Square root of 36**

## Highlights of Factors of 36

- 36 = 2×2×3×3 = 2
^{2}×3^{2}is the prime factorization of 36. - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- The prime factors of 36 are 2 and 3.
- Negative factors of 36 are –1, -2, -3, -4, -6, -9, -12, -18, and –36.

## What are the factors of 36?

To find the factors of 36 by the multiplication method, let us write the number 36 multiplicatively in all possible ways. We have:

36 = 1×36 | ∴ 1, 36 are factors of 36 |

36 = 2×18 | ∴ 2, 18 are factors of 36 |

36 = 3×12 | ∴ 3, 12 are factors of 36 |

36= 4×9 | ∴ 4, 9 are factors of 36 |

36 = 6×6 | ∴ 6 is a factor of 36 |

We cannot write 36 multiplicatively in any other way than the above ones, so we will stop right now. Thus we conclude that the factors of 36 are the numbers in brown color.

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

If m is a factor of 36, then -m is also a factor of 36. So all the negative factors of 36 are -1, -2, -3, -4, -6, -9, -12, -18, and -36.

## Pair Factors of 36

36 = a×b | Factors in Pairs (a,b) |

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) |

Thus the positive pair factors of 36 are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). We know that if (a, b) is a positive pair factor of 36, then (-a, -b) is a negative pair factor of 36. Thus, all the negative pair factors of 36 are given below. They are:

(-1, -36), (-2, -18), (-3, -12), (-4, -9), and (-6, -6).

## Number of factors of 36

From above we have calculated the factors of 36 which are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Thus the total number of factors of 36 is nine.

## Prime Factors of 36

Note that the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Among those factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 36 are 2 and 3.

Question: What are the factors of 36?

Video Solution:

**Also Read:**

Factors of 84: | 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 |

Factors of 56: | 1, 2, 4, 7, 8, 14, 28, 56 |

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

Factors of 48: | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 |

## How to find factors of 36?

Now we will determine the factors of 36 by **division method**. In this method, we will try to find the numbers that can divide 36 with no remainder. See that

36/1=36 and the remainder is 0 | ∴ 1 and 36 are factors of 36 |

36/2=18 and the remainder is 0 | ∴ 2 and 18 are factors of 36 |

36/3=12 and the remainder is 0 | ∴ 3 and 12 are factors of 36 |

36/4=9 and the remainder is 0 | ∴ 4 and 9 are factors of 36 |

36/6=6 and the remainder is 0 | ∴ 6 is a factor of 36 |

Note that no numbers other than the numbers in violet color can divide 36. So the numbers in violet color, that is, 1, 2, 3, 4, 6, 9, 12, 18, and 36 are the complete list of factors of 36.