## Table of Contents

In mathematics, factors are numbers that can divide another number without leaving a remainder. In this article, we will explore the factors of 120.

## What are the factors of 120?

The factors of 120 are the numbers that divide 120 exactly without leaving a remainder. To find the factors, we can start by dividing it by the smallest prime number, which is 2. If 120 is divisible by 2, then 2 is a factor of 120. Continuing this process, we can divide the resulting quotient by the next prime number, and so on, until we reach the square root of 120.

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

- Divide 120 by 1 equals 120
- Divide 120 by 2 equals 60
- Divide 120 by 3 equals 40
- Divide 120 by 4 equals 30
- Divide 120 by 5 equals 24
- Divide 120 by 6 equals 20
- Divide 120 by 8 equals 15
- Divide 120 by 10 equals 12
- Divide 120 by 12 equals 10
- Divide 120 by 15 equals 8
- Divide 120 by 20 equals 6
- Divide 120 by 24 equals 5
- Divide 120 by 30 equals 4
- Divide 120 by 40 equals 3
- Divide 120 by 60 equals 2
- Divide 120 by 120 equals 1

## Factors of 120 in pairs

Factors can be paired together to form pairs that multiply to give the original number. When multiplied together, each pair gives the product 120. These two tables show the positive and negative pairs of factors of 150. The factors of 120 in pairs are (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), and (10, 12).

### Positive Pair

Multiplication | Pair |
---|---|

1 × 120 | (1, 120) |

2 × 60 | (2, 60) |

3 × 40 | (3, 40) |

4 × 30 | (4, 30) |

5 × 24 | (5, 24) |

6 × 20 | (6, 20) |

8 × 15 | (8, 15) |

10 × 12 | (10, 12) |

### Negative Pair

Multiplication | Pair |
---|---|

-1 × -120 | (-1, -120) |

-2 × -60 | (-2, -60) |

-3 × -40 | (-3, -40) |

-4 × -30 | (-4, -30) |

-5 × -24 | (-5, -24) |

-6 × -20 | (-6, -20) |

-8 × -15 | (-8, -15) |

-10 × -12 | (-10, -120) |

## Prime Factors of 120

Prime factors are the factors of a number that are also prime numbers. To find the prime factors, we can divide them by prime numbers until we cannot divide them further. The prime factors of 120 are 2, 2, 2, 3, and 5. We can write this as 2^{3} * 3 * 5, where the exponent indicates the number of times the prime factor appears. Let’s find out the prime factors

- Divide 120 by 2 = 60
- Divide 60 by 2 = 30
- Divide 30 by 2 = 15
- Divide 15 by 3 = 5
- Divide 5 by 5 = 1

So the calculation of these prime numbers (2^{3} * 3 * 5) returns 120.

## Common Factors of 120:

Common factors are numbers that are shared by two or more given numbers. Let’s find the common factors. To determine the common factors, we can compare the factors with the factors of another number. For instance, if we consider the number 60, the common factors of 120 and 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30.

## Distinct Factors of 120:

Distinct factors refer to the unique factors of a number, excluding any repetitions. The distinct factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. These factors represent the different whole numbers that divide 120 without leaving a remainder.

## FAQs about Factors of 120:

How many factors does 120 have?

The number 120 has a total of 16 factors.

What is the largest factor of 120?

The largest factor of 120 is 120 itself.

Are 120 and 30 multiples of each other?

Yes, 120 is a multiple of 30 as 30 can divide 120 without leaving a remainder.

How can I find all the factors of 120?

To find all the factors of 120, you can divide it by numbers starting from 1 and continuing up to 120. The numbers that divide 120 without leaving a remainder are its factors.

What is the sum of all the factors of 120?

The sum of all the factors of 120 is 360.

What are the factors of 120?

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Is 120 a prime number?

No, 120 is not a prime number because it has factors other than 1 and itself.

How many factors does 120 have?

120 has a total of 16 factors.

What is the largest factor of 120?

The largest factor of 120 is 120 itself.

What are the prime factors of 120?

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

Is 120 a perfect square?

No, 120 is not a perfect square because it cannot be expressed as the square of an integer.

Can 120 be divided evenly by 7?

No, 120 cannot be divided evenly by 7.

What is the sum of the factors of 120?

The sum of the factors of 120 is 360.

What is the product of the factors of 120?

The product of the factors of 120 is 691200.

Can 120 be expressed as a product of prime numbers?

Yes, the prime factorization of 120 is 2^3 * 3 * 5, where 2, 3, and 5 are prime numbers.