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Factors

# Factors of 58 | Prime Factorization of 58 | Factor Tree of 58

Written by Prerit Jain

Updated on: 12 Aug 2023

### Factors of 58 | Prime Factorization of 58 | Factor Tree of 58

Factors of 58: Factors of a number are defined as a set of integers that can divide the given number evenly. They leave no reminders.

58 has 4 factors. Factors of 58 are 1, 2, 29, and 58.

The factors of 58 are both positive and negative. They can also occur in pairs. This means that multiplying the numbers within the pairs gives the original number (58) as the product.

In this article, we will discuss the factors of 58 and how to find them using the division method, prime factorization, and factor tree method. Keep reading to know more.

## What Are the Factors of 58?

The factors of 58 are those numbers that divide it evenly, leaving no reminder behind. These factors can be positive or negative.

## What Are the Factors of 58 in Pairs?

Pair factors of 58 are a combination of two numbers, which when multiplied by each other give 58 as the product.

### Positive Pair Factors of 58

The positive pair factors of 58: (1, 58), and (2, 29).

### Negative Pair Factors of 58

The negative pair factors of 58: (-1, -58), and (-2, -29).

## How To Find Factors of 58 Through Division Method?

We will first use the division method to find the factors of 58. As per this approach, we will first divide a sequence of numbers by 58. The numbers that can divide 58 evenly are considered factors of 58. The steps below illustrate how to find the factors of 58 using the division method:

58 ÷ 1 = 58

58 ÷ 2 = 29

58 ÷ 29 = 2

58 ÷ 58 = 1

We can see that 1, 2, 29, and 58 are the numbers that do not leave any remainder when divided by 58. Thus, they are the factors of 58.

## What is the prime factorization of 58?

Before using prime factorization we must check if the given number is a prime number. If it is a prime number, then it has only two factors: 1 and 58. If not, it has more than two factors.

We know that 58 is the composite number. So, it has more than two factors.

The steps to find prime factors of 58 using the prime factorization method are given below:

Step 1: Divide the number 58 by the smallest prime number that can divide it. That number is 2.
58 ÷ 2 = 29

Step 2: Now we got 29 as the quotient. Dividing 29 with 29 gives us 1.
29 ÷ 29 = 1

The quotient is 1. Since 1 cannot be divided further, the prime factors of 58 are 29 X 2.

Image representation of the prime factorization of 58:

## What is the Factor Tree of 58?

We can also use the factor tree method to find the factors of 58. We will first place 58 on top of the factor tree. We will then branch it out with its pair factors. We will separate these factors further till all the numbers of the branches are prime numbers.

Step 1: Let’s place 58 on top of the factor tree. Write down one of its pair factors as part of its branches, that is, 2 and 29.

Step 2: Both 2 and 29 happen to be prime numbers. All the branches in the factor tree are now prime numbers.

Hence, circling all the branches, 2 X 29 = 58, which are 58 prime factors.
We can write the factor tree of 58 in many ways.

Below is an image representation of the factor tree of 58

## Solved Examples on Factors of 58

Here are some solved examples of 58 factors:

What is the sum of all the factors of 58?
1, 2, 29, and 58 are the 58 factors.
1 + 2 + 29 + 58 = 90
Hence, 90 is the sum of all 58 factors.

What are the factors and prime factors of 58?
The 58 factors: 1, 2, 29, and 58.
The 58 prime factors: 29 X 2.

What’s the highest common factor between 68 and 58?
The factors of 68 are 1, 2, 4, 17, 34 and 68.
Factors of 58 are 1, 2, 29, and 58.
Hence, from the above, the common factors of 68 and 58 are 1 and 2.
The highest common factor between 68 and 58 is 2.

What’s the greatest common factor between 87 and 58?
The factors of 87 are 1, 3, 29, and 87.
Factors of 58 are 1, 2, 29, and 58.
Hence, from the above, the common factors of 87 and 58 are 1 and 29.
The highest common factor between 87 and 58 is 29.

Is 29 a factor of 58?
Yes, 29 is a factor of 58.
As 58 ÷ 2 = 29.

What are the factors of -58?
The factors of -58 are -1, -2, -29, and -58.

What are the common factors of 58 and 174?
To find the common factors of 58 and 174, we need to find the factors of both numbers.
Factors of 58: 1, 2, 29, and 58
Factors of 174: 1, 2, 3, 6, 29, 58, 87 and 174
Hence the common factors of 58 and 174 are 1, 2, 29, and 58.

What are all the factors of 58?
The factors of 58 are 1, 2, 29, and 58.

What are the factors of 58 that are composite?
Any number which has more than 2 factors is known as a composite number.
The number which has more than 2 factors in factors of 58 is 58.

What factors of 58 are multiples of 2?
The factors of 58 that are multiples of 2 are 2, and 58.
2 x 1 = 2
2 x 29 = 58.

How many 58 factors are odd?
A total of 2 odd numbers are there in factors of 58 and they are 1 and 29.

What are the factors of 80 and 58?
The factors of 58 are 1, 2, 29, and 58.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

What are the common factors of 26 and 58?
To list out the common factors of 26 and 58, we need to find the factors of both numbers.
Factors of 26: 1, 2, 13 and 26
Factors of 58: 1, 2, 29, and 58
From the above, the common factors of 26 and 58 are 1 and 2.

How many different factors are there for the number 58?
A total of 4 factors are there for the number 58 and are 1, 2, 29, and 58.

How many pair factors are there in 58?
A total of 2 pairs are there in factors of 58.

What is the largest factor of 58?
The largest factor of 58 is 58.
The second largest factor of 58 is 29.

## FAQs on Factors of 58

List all the factors of 58
1, 2, 29, and 58 are the 58 factors.

What are the composite factors of 58?
58 is the 58 composite factor. Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 58 in pairs?
(1, 58), and (2, 29) are the 58 factors of pairs.

What are the positive factors for 58?
1, 2, 29, and 58 are the positive factors for 58.

List the first 10 multiples of 58
58, 116, 174, 232, 290, 348, 406, 464, 522 and 580 are the first 10 multiples of 58.
Multiples are set of numbers that can be divided by the given number (58) evenly.

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Written by

Prerit Jain

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