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Factors of 57: Prime Factorization, Methods, Tree, and Examples

Any number can be considered a factor of 57 if it divides 57 fully without leaving any remainder. This number has to be an integer, meaning it can be a positive or negative whole number but not in fractions or decimals. 

To make the calculations easier for yourself, you should be aware of a few basic concepts. This step is not necessary but makes your process of finding factors easier and less time-consuming. 

The first concept is the process of prime and composite numbers. A prime number is a number that is only divisible by one and itself. Composite numbers are other numbers with more than two factors. The second point is that a factor should always be an integer. Any number in decimals or a fraction can never be counted as a factor for a given number. 

Every number has one as its factor. This one will always be a common factor between the factors of any two numbers. Since you know the basic knowledge, we will move towards the calculation methods of factors now. Methods of representing factors and prime factors will also be discussed later in this article. 

Once you go through this article, finding factors for any number would be a piece of cake for you.  

What are the factors of 57?

The factors of 57 are 1, 3, 19, and 57. Factors of 57 are the integers that divide 57 without leaving any remainder.

Thus, these are the only numbers that divide 57 without leaving any remainder. Since these are more than two factors, 57 is an odd composite number

How To Calculate the Factors of 57?

You can calculate the factor 57 by using any of these two methods: division and multiplication. Calculating any number’s factors is the essential step in this chapter.

Division

We can calculate two factors by one successful work through both methods. The largest factor of any even number, other than itself, is going to be half of that number. 

No other number between the half and the number itself will turn out to be the factor of that number. In the case of any odd number, the largest factor would be smaller than the half as well. 

We will first find half of a given number to find factors through the division method. Then we will consider all the numbers from one to half of that given number to divide our given number fully.

If any number does the job, it will be considered a factor along with the quotient you got during your calculations. 

To find factors of 57 through this method, we will first find its half by dividing it by two. Now we will consider all the numbers from 1 and 28.

 Then we will start dividing 57 with the smaller numbers first to find the number which divides 57 exactly, without leaving any remainder. Listed below are all the successful workings for the factors of 57.

\[ \frac{57}{1} = 57 \]

\[ \frac{57}{3} = 19 \]

Through these workings, we extracted all four factors of 57. While dividing the numbers, you don’t necessarily have to include 19 in your list, as you already know it’s a factor.

To find factors through multiplication, you must take two numbers and multiply them together to get your given number as the product

Both these numbers will be smaller or equal to half of your given number to give the required product. They also have to be the whole number.

By the end of successful working, both these numbers will be considered as the factors of that given number. In the end, you will have to add 1 and the number itself in the final list of factors

Multiplication

For finding factors of 57 by multiplication, we will consider all the numbers from 1 to 28. 

We will multiply each number with different numbers to get the product ‘57’. Shown below are the factors of 57 through multiplication. 

3 x 19 = 57

Our final list will include 1 and 57 as well. So we can conclude that factors of 57 are 1, 3, 19, and 57 and that both these methods are easy and reliable for finding factors.

Factors of 57 by Prime Factorization

Prime factorization is a method to find the prime factors of a number. It breaks down a number to its factors until the prime factors are achieved. Prime factors are the factors that are prime numbers.

In the case of prime factorizing a prime number itself, we will divide it by itself to get both of its only factors: prime numbers. 

For prime factorizing a composite number, you will have to do a lot of work. You will start by dividing the given number by the smallest divisible number.

 If the quotient turns out to be a prime number, you will see if the divisor is a prime number or not.

If it’s a prime number, your work will end there. But if any of the divisor’s quotients is not a prime number, you will keep dividing it by the smallest divisible number, other than 1, until you get prime numbers at the end. 

For prime factorizing 57, we will divide it with the smallest divisible number, ‘3’. Our quotient will be 19. Both numbers are prime numbers, meaning the work is completed. 

The diagram of the prime factorization of this number can be seen below:

Figure 1

Factor Tree of 57

A factor tree can be used to find the prime factors of any number and is also used to represent the ways those prime numbers are achieved

Prime factorization is represented in a way similar to the one used for finding LCM, but a factor tree resembles a family tree when made. 

Both these methods have the same purpose. Workings of prime factorization can also be used to make a factor tree for any number.

Making a factor tree of a prime number is easy as you have to extend two lines below it to write one and the number itself below it. 

This completes the factor tree of a prime number, but a factor tree can grow more than just one extension for a composite number. 

For making a factor tree of 57, 57 will be written on top. The smallest divisible number of 57 is three, so we will divide it by 3. Now we will write three by extending one branch below 57, and then we will write the quotient ‘19’ by extending another branch similarly but towards the other side. 

Now both numbers are prime numbers and cannot be divided any further, so the factor tree of 57 will be completed here, marking 3 and 19 as the prime factors of 57.

Factor Tree of 57 is attached below:

Figure 2

Factor of 57 in Pairs 

Factor pair is any pair of numbers that multiply to give us the product of a certain number. These numbers cannot be in decimals or fractions, as both of them will be considered factors by the end.

These pairs can be calculated through the multiplication or division method directly. For the division method, you will find a factor by dividing a particular number with its divisible numbers. 

Then both the quotient and the divisor will be considered factors of that number. Both these factors form a factor pair for that number.

In the multiplication method, two numbers multiply together to give a certain number as their product.

 Both these numbers together form a factor pair of that number. Remember that one and the number itself are always going to start a factor pair for any integer.

Once you calculate factors of 57 through any of these methods, you can write its factor pairs easily. Have a look at the example below:

\[ \frac{57}{1} = 57 \]

\[ \frac{57}{3} = 19 \]

We can say that (3, 19) and (1, 57) form the factor pairs of 57.

Factors of 57 Solved Examples

Example 1

Prove that 57 is a composite number.

Solution 

57 has four factors that prove that it is a composite number.

Example 2

What are positive and negative factor pairs of 57?

Solution 

The positive factor pairs of 57 is given as follows:

(1, 57)

(3, 19)

The negative factor pairs of 57 is given as follows:

(-1, -57)

(-3, -19)

All images/mathematical drawings are made using GeoGebra.

Factors of 56 | Factor List | Factors of 58

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