A number is called a factor of 120 if it completely divides 120 without leaving a remainder. Thus, the factors of 120 are the divisors of 120. Here, we will learn about the factors of 120 and the prime factors of 120.

• Prime factorization of 120: **120 = 2×2×2×3×5 = 2 ^{3}×3×5.**

• Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

• Prime factors of 120: 2, 3 and 5

• Negative factors of 120: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -30, -40, -60, -120

## What are the Factors of 120?

By the multiplication method, we will find the factors of 120. Let us write the number 120 multiplicatively in all possible ways. We definitely have:

120 = 1×120 | 1, 120 are factors of 120 |

120 = 2×60 | 2, 60 are factors of 120 |

120 = 3×40 | 3, 40 are factors of 120 |

120 = 4×30 | 4, 30 are factors of 120 |

120 = 5×24 | 5, 24 are factors of 120 |

120 = 6×20 | 6, 20 are factors of 120 |

120 = 8×15 | 8, 15 are factors of 120 |

120 = 10×12 | 10, 12 are factors of 120 |

We cannot write 120 multiplicatively in any other way. So the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.

We know that m is a factor of 120 if and only if -m is a factor of 120. So all the negative factors of 120 are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -30, -40, -60, -120.

## Pair Factors of 120

120 = a×b | Factors in Pairs (a,b) |

120 = 1×120 | (1, 120) |

120 = 2×60 | (2, 60) |

120 = 3×40 | (3, 40) |

120 = 4×30 | (4, 30) |

120 = 5×24 | (5, 24) |

120 = 6×20 | (6, 20) |

120 = 8×15 | (8, 15) |

120 = 10×12 | (10, 12) |

Thus the positive pair factors of 120 are (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), and (10, 12).

And the negative pair factors of 120 are (-1, -120), (-2, -60), (-3, -40), (-4, -30), (-5, -24), (-6, -20), (-8, -15), and (-10, -12).

## Number of Factors of 120

From above we have calculated the factors of 120 which are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120

Thus the total number of factors of 120 is sixteen.

## Prime Factors of 120

Note that the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. Among these factors, we observe that only 2, 3, and 5 are prime numbers as they do not have any proper divisors.

∴ The prime factors of 120 are 2, 3, and 5.

**Also Read:**

Factors of 100: | 1, 2, 4, 5, 10, 20, 25, 50, 100 |

Factors of 108: | 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 |

Factors of 90: | 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 |

Factors of 128: | 1, 2, 4, 8, 16, 32, 64, 128 |

Question: What are the factors of 120?

Video Solution:

## How to Find Factors of 120?

Now we will determine the factors of 120 by **division method**. In this method, we will try to find the numbers that can divide 120 with no remainder.

120/1=120 and the remainder is 0. | ∴ 1 and 120 are factors of 120. |

120/2=60 and the remainder is 0. | ∴ 2 and 60 are factors of 120. |

120/3=40 and the remainder is 0. | ∴ 3 and 40 are factors of 120. |

120/4=30 and the remainder is 0. | ∴ 4 and 30 are factors of 120. |

120/5=24 and the remainder is 0. | ∴ 5 and 24 are factors of 120. |

120/6=20 and the remainder is 0. | ∴ 6 and 20 are factors of 120. |

120/8=15 and the remainder is 0. | ∴ 8 and 15 are factors of 120. |

120/10=12 and the remainder is 0. | ∴ 10 and 12 are factors of 120. |

Note that no numbers other than the numbers in violet color can divide 120. So the numbers in violet color, that is, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. are the complete list of factors of 120.

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