Factors of 57 are the numbers which when multiplied in pairs give the product as 57. These factors can be negative as well. The number 57, like a few special two-digit numbers, is the product of two prime numbers, i.e., 3 and 19. In this lesson, we will calculate the factors of 57, prime factors of 57, and factors of 57 in pairs along with solved examples for a better understanding.

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Factors of 57: 1, 3, 19, and 57Prime Factorization of 57: 57 = 3 × 19
1.What Are the Factors of 57?
2.How to Calculate Factors of 57?
3.Factors of 57 by Prime Factorization
4.Factors of 57 in Pairs
5.FAQs on Factors of 57

What Are the Factors of 57?

The numbers by which 57 is divisible are the factors of 57. When the factors of 57 divide 57, the remainder is 0. For example, when 57 is divisible by 19, you get the remainder as 0 and the quotient as 3.

Hence, 19 is a factor of 57. 

Here, the quotient is 3. Notably, 3 is also a factor of 57. Do you know why?


How to Calculate the Factors of 57?


In the last section, we learned that the factors of 57 can be found through division. We can find the factors of 57 through multiplication as well. Can you think of two numbers whose product is 57? Can you think of all such possibilities?

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The multiplicands of each such product are the factors of 57. Thus, the factors of 57 are 1, 3, 19, and 57.

Tips and Tricks:

By dividing a number by its factor, we can find another factor (which is the quotient of the division).An odd number cannot have even factors.Divisibility rules make the process of finding factors easy.

Explore factors using illustrations and interactive examples.


Factors of 57 by Prime Factorization

The prime factorization of 57 is the product of prime numbers which results in 57.

So the prime factorization of 57 is 57 = 3 × 19

From the prime factorization of 57, it is clear that 3 and 19 are the prime factors of 57.

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We know that 1 is the factor of every number. Thus, the factors of 57 by prime factorization are 1, 3, 19, and 57. How to find the composite factors of a number when its prime factorization has more than 2 multiplicands? Let"s see.

Factors of 60

The prime factorization of 60 is 60 = 2 × 2 × 3 × 5

Using the same procedure as above:

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Now that we have done the prime factorization of 57, we can multiply it and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.


Factors of 57 in Pairs

The pair factors of 57 are obtained by writing 57 as a product of two numbers in all possible ways. In each product, both multiplicands together make a pair factor of 57.

Factors

Pair Factors 

1 × 57 = 57

 (1, 57)

3 × 19 = 57

 (3, 19)

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The negative pair factors of 57 are (-1, -57) and (-3, -19).

Challenging Questions:

James has 60 green candies and Mark has 90 blue candies. They want to arrange the candies in such a way that each row contains an equal number of candies and also each row should have only either green candies or blue candies. What is the greatest number of candies that can be arranged in each row?Hint: Find the factors of each of 60 and 90. Identify common factors. Then identify the highest number among the common factors. 

Factors of 57 Solved Examples


Example 1: Olivia is trying to find the maximum number that can divide both 60 and 75. Can we help her?

Solution:

A number that divides the given number is a factor of the given number.

To solve the given problem, we have to write the factors of each of 60 and 75.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

The factors of 75 are 1, 3, 5, 15, 25, 75.

Thus, the maximum number that can divide both 60 and 75 is 15.


Example 2: Mathew, a yoga teacher, wants to divide a batch of his students comprising 57 students into groups such that:

No group has 1 or all the students.

Each group should have at least 5 students.

Each group should have an equal number of students.

Then what can be the size(s) of each group?

Solution:

Since each group should have an equal number of students, we have to use the factors of 57 to solve this problem.

The factors of 57 are 1, 3, 19, and 57.

Since a group cannot have 1 or all the students, the size of the group cannot be 1 or 57.

Since each group should have at least 5 students, the size of the group cannot be 3 as well.

Thus, the size of each group = 19.


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FAQs on Factors of 57

What are the factors of 57?

The factors of 57 are 1, 3, 19, and 57.

Is 57 a prime or composite?

The factors of 57 are 1, 3, 19, and 57.

It has more than two factors.

Hence it is a composite number.

What are the factors of 56?

The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

What are the common factors of 57 and 19?

The factors of 57 are 1, 3, 19, and 57.

The factors of 19 are 1 and 19.

Hence the common factors are 1 and 19.

See more: What Is The Measure Of Ria ?

What are the common factors of 57 and 76?

The factors of 57 are 1, 3, 19, and 57.