Factors of 58
Factors of 58 are the numbers which when multiplied in pairs give the product as 58. 58 has many factors and it is a composite number. In this lesson, we will learn how to find the factors of 58, the prime factors of 58, and the factors of 58 in pairs along with solved examples for a better understanding.
 Factors of 58: 1, 2, 29 and 58
 Prime Factorization of 58: 2 × 29
1.  What Are the Factors of 58? 
2.  How to Calculate the Factors of 58? 
3.  Factors of 58 by Prime Factorization 
4.  Factors of 58 in Pairs 
5.  FAQs on Factors of 58 
What Are the Factors of 58?
The factors of 58 are the numbers that divide 58 leaving 0 as the remainder.
For example, when 58 is divided by 29, the remainder is 0. Hence, 29 is a factor of 58.
Explore factors using illustrations and interactive examples:
 Factors of 360: The factors of 36 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
 Factors of 24: The factors of 24 are1, 2, 3, 4, 6, 8, 12, and 24.
 Factors of 6: The factors of 6 are 1, 2, 3, and 6.
 Factors of 180: The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
 Factors of 45: The factors of 45 are 1, 3, 5, 9, 15, and 45.
How to Calculate the Factors of 58?

We can find the factors of 58 using multiplication as well.

Can you think of two numbers whose product is 58? Can you think of all such possibilities?
The multiplier and the multiplicand in each case are the factors of 58. The factors of 58 are 1, 2, 29, and 58.
Factors of 58 by Prime Factorization
The prime factorization of 58 refers to the method of expressing 58 as the product of its prime numbers.
 The prime factorization of 58 is 58 = 2 × 29.
 From the prime factorization of 58, it is clear that 2 and 29 are the prime factors of 58.
Tips And Tricks
The number of factors that a particular number has can be found using the following steps:
 Find the prime factorization of the number and express it in the exponent form.
 Add 1 to each of the exponents.
 Multiply all numbers that are obtained from step 2.
 The resultant product would give the number of factors.
Factors of 58 in Pairs
The pair factors of 58 are obtained by writing 58 as a product of two numbers in all possible ways.
In each product, both the multiplicands are the pair factors of 58.
Product that Results in 58 
Factors of 58 in pairs 

1 × 58 
(1, 58) 
2 × 29 
(2, 29) 
Important Notes
 Every number (except 1) has a minimum of two factors, 1 and the number itself.
 A prime number has exactly two factors.
 A composite number has more than two factors.
Factors of 58 Solved Examples

Example 1: Emma is trying to arrange 58 matchsticks in rows such that each row has an equal number of matchsticks. But she doesn't want all the matchsticks to be in the same row or the same column. In how many ways can she arrange the matchsticks?
Solution:
The factors of 58 are 1, 2, 29 and 58.
Since all the matchsticks cannot be in a single row or column, we will ignore the factors 1 and 58.
The other factors of 58 are 2 and 29.
Thus, she can arrange the matchsticks in 2 different ways.

Example 2: Nicolas was asked to find the common factors of 58 and 60. Can we help him with this?
Solution:
The factors of 58 are 1, 2, 29 and 58.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Thus, the common factors of 58 and 60 are 1 and 2.
FAQs on Factors of 58
What are the factors of 58?
Divide it by 1, 2, 3, ...up to 29 (half of 58). The numbers that completely divide 58 are the factors of 58.
Thus, the factors of 58 are 1, 2, 29, and 58.
What are the factors of 58 and 59?
The factors of 58 are 1, 2, 29, and 58.
The factors of 59 are 1 and 59.
Is 58 a perfect number?
The factors of 58 are 1, 2, 29, and 58. The sum of all its factors except itself is 1 + 2 + 29 = 32.
This sum is not 58. Thus, 58 is NOT a perfect number.
What factors of 58 add up to 60?
The factors of 58 are 1, 2, 29, and 58. The factors 58 and 2 add up to 60.
How to find the prime factors of 58?
The prime factors are found by the prime factorization of 58 either by division method or by the factor tree method. The prime factors of 58 are 2 and 29.
58 = 2 × 29