# Factors of 58

Factors of 58 are 1, 2, 29, and 58

#### How to find factors of a number

 1.   Find factors of 58 using Division Method 2.   Find factors of 58 using Prime Factorization 3.   Find factors of 58 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 58

• Divide 58 by 1: 58 ÷ 1 : Remainder = 0
• Divide 58 by 2: 58 ÷ 2 : Remainder = 0
• Divide 58 by 29: 58 ÷ 29 : Remainder = 0
• Divide 58 by 58: 58 ÷ 58 : Remainder = 0

Hence, Factors of 58 are 1, 2, 29, and 58

#### 2. Steps to find factors of 58 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 58 using the division method, follow these steps:

• Step 1. Start dividing 58 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 58, which is 2. Divide 58 by 2 to obtain the quotient (29).
58 ÷ 2 = 29
• Step 3. Repeat step 1 with the obtained quotient (29).
29 ÷ 29 = 1

So, the prime factorization of 58 is, 58 = 2 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 58 as shown below:

So, the prime factorization of 58 is, 58 = 2 x 29.

#### 3. Find factors of 58 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 58 would be the two numbers which, when multiplied, give 58 as the result.

The following table represents the calculation of factors of 58 in pairs:

Factor Pair Pair Factorization
1 and 58 1 x 58 = 58
2 and 29 2 x 29 = 58

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 58. They are called negative pair factors.

Hence, the negative pairs of 58 would be ( -1 , -58 ) , ( -2 , -29 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 58 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 29, 58 are exact divisors of 58.
• 1 is a factor of every number. Eg. 1 is a factor of 58.
• Every number is a factor of zero (0), since 58 x 0 = 0.

• Is 58 a perfect square?

No 58 is not a perfect square.

• What are factors of 58?

Factors of 58 are 1, 2, 29, 58.

• Which is greatest factor of 58?

The greatest factor of 58 is 29.

• What is the sum of all factors of 58?

The sum of all factors of 58 is 90.

• What are multiples of 58?

First five multiples of 58 are 116, 174, 232, 290.

• What is the greatest prime factors of 58?

The greatest prime factor of 58 is 29.

• What are six multiples of 58?

First five multiples of 58 are 116, 174, 232, 290, 348, 406.

• What is prime factorization of 58?

Prime factorization of 58 is 2 x 29.

• Is 58 a whole number?

Yes 58 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 58? Help her in writing all the factors.

Positive factors are 1, 2, 29, 58.
Negative factors are -1, -2, -29, -58.

Can you help Sammy find out the product of the odd factors of 58?

Factors of 58 are 1, 2, 29, 58.
Odd factors of 58 are 1, 29.
Hence product of odd factors of 58 is; 1 x 29 = 29.

Joey wants to write all the prime factors of 58 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 58 are 2, 29.
So in exponential form it can be written as 2 x 29.

How many factors are there for 58?

Factors of 58 are 1, 2, 29, 58.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 58. Can you predict the answer?

3 factor(s) of 58 are 1, 2, 29.

Sammy is puzzled while calculating the prime factors of 58. Can you help him find them?

Factors of 58 are 1, 2, 29, 58.
Prime factors of 58 are 2, 29

What is prime factorization of 58?

Prime factorization of 58 is 2 x 29 = 2 x 29.