## Table of Contents

Factors are the numbers that can be multiplied together to obtain a given number. In the case of 150, there are several factors that can be found by dividing 150 by different numbers. Let’s explore the factors of 150 and their properties.

## What are the Factors of 150?

The factors of 150 are the numbers that divide evenly into 150 without leaving a remainder. Let’s find out.

- Divide 150 by 1 equals 150
- Divide 150 by 2 equals 75
- Divide 150 by 3 equals 50
- Divide 150 by 5 equals 30
- Divide 150 by 6 equals 25
- Divide 150 by 10 equals 15
- Divide 150 by 15 equals 10
- Divide 150 by 25 equals 6
- Divide 150 by 30 equals 5
- Divide 150 by 50 equals 3
- Divide 150 by 75 equals 2
- Divide 150 by 150 equals 1

Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. These numbers can be multiplied together to get the product 150.

## Factors of 150 in Pairs

Factors can be paired up in such a way that when multiplied, they give the original number. Pairs of factors of 150 are given into positive and negative sides below:

### Positive Pair

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

1 × 150 | (1, 150) |

2 × 75 | (2, 75) |

3 × 50 | (3, 50) |

5 × 30 | (5, 30) |

6 × 25 | (6, 25) |

10 × 15 | (10, 15) |

### Negative Pair

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

-1 × -150 | (-1, -150) |

-2 × -75 | (-2, -75) |

-3 × -50 | (-3, -50) |

-5 × -30 | (-5, -30) |

-6 × -25 | (-6, -25) |

-10 × -15 | (-10, -15) |

## Prime Factors of 150

Prime factors are the factors of a number that are prime numbers. To find the prime factors of 150, we divide them by prime numbers until we cannot divide them any further. Let’s find it out.

Step1: Divide 150 by 2 equals 75

Step2: Divide 75 by 3 equals 25

Step3: Divide 25 by 5 equals 5

Step4: Divide 5 by 5 equals 1

The prime factors of 150 are 2, 3, 5, and 5. This can be expressed as the prime factorization: 2 x 3 x 5 x 5. The calculation of 2 x 3 x 5 x 5 equals 150.

Understanding the factors of 150 is useful in various mathematical concepts, such as finding common multiples, simplifying fractions, and solving equations. Factors play a significant role in number theory and have practical applications in fields like mathematics, engineering, and cryptography.

Remember, factors are not limited to positive integers. Negative integers and fractions can also be factors of a number. The concept of factors helps in analyzing the properties and relationships between numbers, leading to a deeper understanding of mathematics as a whole.

## Frequently Asked Questions

What are the factors of 150?

The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

What are the factors of 75?

The factors of 75 are 1, 3, 5, 15, 25, and 75.

Are 150 and 75 multiples of each other?

Yes, 150 is a multiple of 75 because 150 divided by 75 equals 2. Similarly, 75 is a multiple of 150 because 75 divided by 150 equals 0.5.

Can 150 be evenly divided by 4?

No, 150 cannot be evenly divided by 4 because there is a remainder when you divide 150 by 4.

What is the greatest common factor (GCF) of 150 and 75?

The greatest common factor of 150 and 75 is 75.

What is the least common multiple (LCM) of 150 and 75?

The least common multiple of 150 and 75 is 300.

Can 150 be expressed as a product of prime factors?

Yes, the prime factorization of 150 is 2 * 3 * 5^{^2}, where “^” denotes exponentiation.

What are the factors of other numbers like 100, 200, and 300?

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.

The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.

What are the factors of 150?

The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

Is 150 a prime number?

No, 150 is not a prime number because it has factors other than 1 and itself.

How many factors does 150 have?

150 has a total of 12 factors.

What is the largest factor of 150?

The largest factor of 150 is 150 itself.

What are the prime factors of 150?

The prime factors of 150 are 2, 3, 5, and 25.

Is 150 a perfect square?

No, 150 is not a perfect square because it cannot be expressed as the square of an integer.

Can 150 be divided evenly by 7?

No, 150 cannot be divided evenly by 7.

What is the sum of the factors of 150?

The sum of the factors of 150 is 366.

What is the product of the factors of 150?

The product of the factors of 150 is 562500.

Can 150 be expressed as a product of prime numbers?

Yes, the prime factorization of 150 is 2 * 3 * 5^2, where 2, 3, and 5 are prime numbers.