Factors

# Factors of 50 | Prime Factorization of 50 | Factor Tree of 50

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### Factors of 50 | Prime Factorization of 50 | Factor Tree of 50

**Factors of 50:** The factors of a number are a set of integers, that can divide a given number evenly. They leave behind no reminder.

**The number 50 has 6 factors. Factors of 50 are 1, 2, 5, 10, 25, and 50.**

The factors of 50, like that of all numbers, are both positive and negative. They can also be written as pairs. When the paired factors are multiplied by each other, the product equals 50.

In this article, we will talk about how to find the factors of 50 using the division method, prime factorization, and factor tree. Keep reading to know more.

## What Are the Factors of 50?

The factors of 50 are those integers that can divide 50 evenly, leaving behind no reminder. These factors can be both positive and negative.

Factors of 50: 1, 2, 5, 10, 25 and 50 |

Negative Factors of 50: -1, -2, -5, -10, -25 and -50 |

Prime Factorization of 50: 5 X 5 X 2 |

Pair Factors of 50: (1, 50); (2, 25) and (5, 10) |

Prime Factors of 50: 2, 5 |

Sum of Factors of 50: 93 |

Sum of Prime Factors of 50: 7 |

### What Are the Factors of 50 in Pairs?

A pair factor of 50 is a set of two numbers, which when multiplied by each other give 50 as the product. These pair factors can also be positive or negative as shown in the table below:

### Positive Pair Factors of 50

**Positive pair factors of 50: (1, 50), (2, 25), and (5, 10).**

### Negative Pair Factors of 50

**Negative pair factors of 50: (-1, -50), (-2, -25) and (-5, -10).**

### How To Find Factors of 50 Through Division Method?

We will use the division method to find the factors of 50. In this approach, we will divide 50 with a sequence of integers. The numbers that divide 50 evenly, without leaving any reminders are the factors of 50. The steps given below illustrate the method to find the factors of 50 using the division method:

• 50 ÷ 1 = 50

• 50 ÷ 2 = 25

• 50 ÷ 5 = 10

• 50 ÷ 10 = 5

• 50 ÷ 25 = 2

• 50 ÷ 50 = 1

Therefore, we can see that 1, 2, 5, 10, 25, and 50 are the numbers that do not leave any remainder when divided by 50.

### What Is the Prime Factorization of 50?

To perform the prime factorization, we must first check if the given number is a prime number. If the is a prime number, it has only two factors: 1 and 50. If the number is composite, it has over two factors.

We know that 50 is the composite number. So, it has over two factors. We can use prime factorization to find the factors of 50.

The following steps illustrate the method to find the factors of 50 using prime factorization:

**Step 1:** Divide the number 50 by the smallest prime number that can divide it. We know that this number is 2.

50 ÷ 2 = 25

**Step 2:** The quotient is 25. Divide 25 by the smallest prime number that can divide it. This number is 5.

25 ÷ 5 = 5

**Step 3:** We got 5 as the quotient. Dividing 5 with 5 gives us 1.

5 ÷ 5 = 1

The quotient is 1. But it cannot be divided any further. So, the prime factors of 50 are 5 X 5 X 2 or 52 X 2.

Image representation of the prime factorization of 50:

### What is the Factor Tree of 50?

We will be using the factor tree method to find the factors of 50. We will start by placing 50 on top of the tree. As part of its branches, we will select a set of its factor pairs. These pairs will be divided further till all the branches have prime numbers.

**Step 1:** Let’s place 50 at the top of the factor tree. As part of its branches, write down 2 and 25.

**Step 2:** 2 is a prime number and cannot be separated any further. We will now divide 25 into 5 and 5.

**Step 3:** We can see that 5 is a prime number. So, all the branches of the factor tree contain prime numbers. This brings us to the end of the factor tree.

Thus, 25 X 2 or 5 X 5 X 2 = 50 are the prime factors of 50.

Below is a visual representation of the factor tree of 50, choosing 2 and 25 as the pair factors.

**Solved Examples of Factors of 50**

Here are some solved examples of 50 factors:

**What is the sum of all the factors of 50?**1, 2, 5, 10, 25 and 50 are the factors of 50.

1 + 2 + 5 + 10 + 25 + 50 = 93

The sum of all the factors of 50 is 93.

**What are the factors and prime factors of 50?**Factors of 50: 1, 2, 5, 10, 25 and 50.

Prime factors of 50: 25 X 2 or 5 X 5 X 2.

**What’s the highest common factor between 60 and 50?**The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Factors of 50 are 1, 2, 5, 10, 25 and 50.

The common factors of 60 and 50 are 1, 2, 5 and 10.

The highest common factor between 60 and 50 is 10.

**What’s the highest common factor between 50 and 100?**The factors of 50 are 1, 2, 5, 10, 25 and 50.

Factors of 100 are 1, 2, 4, 5, 10,20, 25, 500 and 100.

Hence, from the above, the common factors of 50 and 100 are 1, 2, 5, 10 and 25.

The highest common factor between 50 and 100 is 25.

**Is 25 a factor of 50?**Yes, 25 is a factor of 50.

As 50 ÷ 2 = 25.

**What are the factors of -50?**The factors of -50 are -1, -2, -5, -10, -25 and -50.

**What are the common factors of 50 and 70?**To find the common factors of 50 and 70, we need to find the factors of both numbers.

Factors of 50: 1, 2, 5, 10, 25 and 50

Factors of 70: 1, 2, 5, 7, 10, 14, 35 and 70

Hence the common factors of 50 and 70 are 1, 2, 5 and 10.

**What are all the factors of 50?**The factors of 50 are 1, 2, 5, 10, 25 and 50.

**What are the factors of 50 that are composite?**Any number which has more than 2 factors is known as a composite number. The list of numbers which has more than 2 factors in factors of 10, 25 and 50.

**What factors of 50 are multiples of 5?**The factors of 50 that are multiples of 5 are 5, 10, 25 and 50.

5 x 1 = 5

5 x 2 = 10

5 x 5 = 25

5 x 10 = 55.

**How many 50 factors are odd?**A total of 4 odd numbers are there in factors of 50 and 1, 5, 25 and 50.

**What are the factors of 50 and 30?**The factors of 50 are 1, 2, 5, 10, 25 and 50.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and of 30.

**What are the common factors of 50 and 75?**To list out the common factors of 50 and 75, we need to find the factors of both numbers.

Factors of 50: 1, 2, 5, 10, 25 and 50

Factors of 75: 1, 3, 5, 15, 25 and 75

From the above, the common factors of 50 and 75 are 1, 5 and 25.

**How many different factors are there for the number 50?**A total of 6 factors are there for the number 50 and they are 1, 2, 5, 10, 25 and 50.

**What factors of 50 are multiples of 2?**The factors of 50 that are multiples of 2 are 2, 10 and 50.

**How many pair factors are there in 50?**A total of 3 pairs are there in factors of 50.

**What is the largest factor of 50?**The largest factor of 50 is 50.

The second largest factor of 50 is 25.

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### FAQs on Factors of 50

**List all the factors of 50**1, 2, 5, 10, 25 and 50 are the 50 factors.

**What are the composite factors of 50?**10, 25 and 50 are the 50 composite factors.

Composite factors are those that have more than 2 factors other than 1 and itself.

**What are the factors of 50 in pairs?**(1, 50), (2, 25) and (5, 10) are the 3 pair of factors.

**What are the positive factors for 50?**1, 2, 5, 10, 25, and 50 are the positive factors for 50.

**What are the negative factors of 50?**The negative factors of 50 are -1, -2, -5, -10, -25 and -50

We have covered all the necessary information regarding the factors of 50. We hope that this blog has proven useful and easy to understand.

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Written by

Prerit Jain