# Factors of 58

The factors of 58 are the numbers that divide 58 evenly without leaving any remainder. The factors and the pair factors of 58 can be expressed in positive as well as in negative form, but it cannot be expressed in decimal or fractional form. For example, the pair factors of 58 are represented as (1, 58) or (-1, -58). If we multiply a pair of negative numbers, such as multiplying -1 and -58, it will result in the original number 58. In this article, we are going to discuss what are the factors of 58, positive and negative pair factors of 58, and how to find the prime factors of 58 using the prime factorization method and many solved examples.

## What are the Factors of 58?

The numbers that divide 58 evenly and leave a remainder 0 are the factors of 58. In other words, the numbers that are multiplied together in pairs, resulting in the original number 58 are the factors of 58. As 58 is an even composite number, it has more than two factors. Therefore, the factors of 58 are 1, 2, 29 and 58. Similarly, the negative factors of 58 are -1, -2, -29 and -58.

 Factors of 58: 1, 2, 29 and 58. Prime Factorization of 58: 2 × 29.

## Pair Factors of 58

A pair of numbers that are multiplied together resulting in the number 58 are the pair factors of 58. The following are the positive and negative pair factors of 58.

Positive Pair Factors of 58:

 Positive Factors of 58 Positive Pair Factors of 58 1 × 58 (1, 58) 2 × 29 (2, 29)

Therefore, the positive pair factors of 58 are (1, 58) and (2, 29).

Negative Pair Factors of 58:

 Negative Factors of 58 Negative Pair Factors of 58 -1 × -58 (-1, -58) -2 × -29 (-2, -29)

Therefore, the negative pair factors of 58 are (-1, -58) and (-2, -29).

## Factors of 58 by Division Method

The factors of 58 are found using the division method. In this method, the number 58 is divisible by different integers. If the integer divides 58 evenly without leaving any remainder, then those integers are the factors of 58. Now, let us discuss how to find the factors of 58 using the division method.

• 58/1 = 58 (Factor is 1 and Remainder is 0)
• 58/2 = 29 (Factor is 2 and Remainder is 0)
• 58/29 = 2 (Factor is 29 and Remainder is 0)
• 58/58 = 1 (Factor is 58 and Remainder is 0)

If we divide 58 by any numbers other than 1, 2, 29 and 58, it leaves a remainder value. Hence the factors of 58 are 1, 2, 29 and 58.

## Prime Factorization of 58

In the prime factorization of 58, the number 58 is written in the form of the product of its prime factors. Go through the following procedure to find the prime factors of 58.

Take a pair factor of 58, say (1, 58). Here the number 58 is an even composite number, which can be split further into its prime factors.

So, find the two numbers which on multiplication results in the original number 58.

Thus, 58 is written as the product of 2 and 29, where 2 and 29 are prime numbers.

Therefore, the prime factorization of 58 is 2 × 29.

### Solved Examples

Example 1:

Find the common factors of 58 and 59.

Solution:

The factors of 58 are 1, 2, 29 and 58.

The factors of 59 are 1 and 59.

Therefore, the common factor of 58 and 59 is 1.

Example 2:

Find the common factors of 58 and 57.

Solution:

Factors of 58 = 1, 2, 29 and 58.

Factors of 57 = 1, 3, 19 and 57.

Thus, the common factor of 58 and 57 is 1.

Example 3:

Find the common factors of 58 and 29.

Solution:

The factors of 58 are 1, 2, 29 and 58.

The factors of 29 are 1 and 29.

Hence, the common factors of 58 and 29 are 1 and 29.

## Frequently Asked Questions on Factors of 58

### What are the factors of 58?

The factors of 58 are 1, 2, 29 and 58.

### What is the prime factorization of 58?

The prime factorization of 58 is 2 × 29.

### What are the positive pair factors of 58?

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

### What are the negative pair factors of 58?

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

### Is 29 a factor of 58?

Yes, 29 is a factor of 58. If 58 is divisible by 29, it leaves a quotient of 2 and remainder 0, and hence, 29 is a factor of 58.