Factors

# Factors of 59 | Prime Factorization of 59 | Factor Tree of 59

Written by Prerit Jain

Updated on: 12 Aug 2023

### Factors of 59 | Prime Factorization of 59 | Factor Tree of 59

Factors of 59: Factors are a set of integers that can divide a given number evenly, without leaving a reminder.

The number 59 is a prime number. It has only two factors – 1 and 59.

Factors can be written in both positive and negative formats. They can also occur as pairs. This means that multiplying the numbers within the pairs will yield a product that equals the given number.

## What Are the Factors of 59?

The factors of 59, like that of other numbers, divide 59 evenly without leaving any remainder. The factors can be positive and negative. Hence, the number 59 has both positive and negative factors.

## What Are the Factors of 59 in Pairs?

The pair factors of 59 are a combination of two numbers, which when multiplied by each other give 59 as a product. These pair factors are also written in positive and negative pairs as shown in the table below:

### Positive Pair Factors of 59

Positive pair factor of 59: (1, 59).

### Negative Pair Factors of 59

Negative pair factor of 59: (-1, -59)

## How To Find Factors of 59 Through Division Method?

We are using the division method to determine the factors of 59. As per this approach, we will multiply 59 with a sequence of natural numbers. The numbers that divide 59 evenly are known as its factors. The following steps give a detailed account of how to find the factors of 59 using the division method:

59 ÷ 1 = 59

59 ÷ 59 = 1

We can see that 1 and 59 are the numbers that do not leave any remainder when divided by 59. So, they are the factors of 59.

## What Is the Prime Factorization of 59?

Before we use the prime factorization method, we must check if the given number is a prime number. If the number is a prime number, then it has only two factors: 1 and 59. If not, then it has more than two factors.

59 is a prime number. It has only two factors. But let us employ the prime factorization method to present a better understanding of the concept.

The steps below help find the factors of 59 using the prime factorization method are given below:

Step 1: Divide 59 by the smallest prime number that can divide it. This number is 59.

59 ÷ 59 = 1

Step 2: Now we got 1 as the quotient. This brings us to the end of the factor tree.

Since 1 cannot be divided further, the prime factor of 59 is 591.

Image representation of the prime factorization of 59:

## What is the Factor Tree of 59?

The third method of finding the factors of 59 is the factor tree method. This method will place the number 59 on top of the factor tree. Now, as part of the branches, we will write down any set of pair factors of the given number (59). We will again split the pair of factors into factors. This process will go on until the branches become prime numbers.

Step 1: Let’s place the number 59 at the top of the factor tree. Since it is a prime number, the only two factors of 59 are 1 and 59.

Step 2: We cannot separate these numbers into branches anymore. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 591 or 59 X 1 = 59, which are 59 prime factors.

Below is an image representation of the factor tree of 59.

## Solved Examples of Factors of 59

Here are some solved examples of 59 factors:

What is the sum of all the factors of 59?
1 and 59 are the 59 factors.
1 + 59 = 60
Hence, 60 is the sum of all 59 factors.

What are the factors and prime factors of 59?
The factors of 59: 1 and 59.
The prime factors of 59: 59 X 1 or 591.

What’s the highest common factor between 59 and 82?
The factors of 59 are 1 and 59.
Factors of 82 are 1, 2, 41, and 82.
Hence, from the above, the highest and only common factor of 59 and 82 is 1.

What’s the highest common factor between 24 and 59?
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Factors of 59 are 1 and 59.
Hence, from the above, the highest and the only common factors of 24 and 59 is 1.

Is 177 a factor of 59?
No, 177 is not a factor of 59. It is a multiple of 59. Multiples are those numbers that can be divided by a given number evenly.
As 177 ÷ 59 = 3.

What are the factors of -59?
The factors of -59 are -1 and -59.

What are the common factors of 59 and 54?
To find the common factors of 59 and 54, we need to find the factors of both numbers.
Factors of 59: 1 and 59
Factors of 54: 1, 2, 3, 6, 9, 18, 27 and 54
Hence the common factor of 59 and 54 is 1.

What are all the factors of 59?
The factors of 59 are 1 and 59.

What are the factors of 59 that are composite?
Any number which has more than 2 factors is known as a composite number. 59 does not have any composite factors.

How many 59 factors are odd?
All factors of 59 are odd. They are 1 and 59.

How many different factors are there for the number 59?
A total of 2 factors are there for the number 59 and they are 1 and 59.

How many pair factors are there in 59?
A total of 1 pair is there in factors of 59.

What is the largest factor of 59?
The largest factor of 59 is 59.
The second largest factor of 59 is 1.

## FAQs on Factors of 59

List all the factors of 59
1 and 59 are the 59 factors.

What are the composite factors of 59?
Composite factors are those that have more than 2 factors other than 1 and itself. 59 does not have any composite factors.

What are the factors of 59 in pairs?
(1, 59) are the 59 factors of pairs.

What are the positive factors for 59?
1 and 59 are the positive factors for 59.

What are the negative pair factors of 59?
The negative pairs of 59 are (-1, -59)

We have now learned all the methods to calculate factors of 59.

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Written by by

Prerit Jain

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