Is 57 a Prime Number

In mathematics, we have different types of numbers such as rational, irrational, whole numbers, integers, natural numbers, even numbers, odd numbers, etc. All these numbers are defined based on certain criteria. Similarly, we have prime numbers which are defined based on the number of factors of the given number. All natural numbers are categorized into either prime or composite numbers except 1. Also, prime numbers are always odd numbers. However, 2 is the only even prime number. In this article, you will learn how to check whether the given number is prime or not, along with the formulas and different methods.

Is 57 a prime number? Before answering this question, let’s understand what a prime number is and how to identify whether a number is prime or not. First, there are numbers, having exactly two factors 1 and the number itself. Such numbers are 2, 3, 5, 7, 11, etc. These numbers are prime numbers. Mathematically, the numbers other than 1, whose only factors are 1 and the number itself, are called Prime numbers. In contrast, numbers having more than two factors are called Composite numbers. For example, the numbers 4, 6, 8, 10, 12, etc., are composite. However, 1 is neither a prime nor a composite number.

Is 57 Prime or Composite?

In the above section, you have learned what a prime and composite number are. Now the question is whether the number 57 is prime or not. 57 is not a prime number. By the definition of prime numbers, if a number has only 2 factors, i.e. 1 and the number itself, then it is a prime number. If the number has more than 2 factors, then it is called a composite number. Here, the number 57 contains more than two factors.

Why is 57 not a Prime Number?

To understand how 57 does not become a prime number, one should find the factors of 57. As we know, the factors of any number can be found either by the prime factorisation method or the division method. In both of these cases, we get a pair of numbers that get multiplied and produce the result as the original number. Thus, the pairs of numbers, which produce 57 on multiplication are given as:

1 × 57 = 57

3 × 19 = 57

Or

57 × 1 = 57

19 × 3 = 57

The unique numbers in the above pairs are the factors for 57, i.e. 1, 3, 19 and 57.

That means the number 57 has more than two factors. Hence, 57 is not a prime number but a composite number.

Click here to know more about factors.

Also, get the related questions on the classification of the number 57 in the table given below:

Let’s have a look at the prime numbers chart below to know which numbers before and after 57 are prime numbers that are below 100. This chart helps in answering many questions based on identifying the prime numbers between 1 and 100.

From the above, one can answer the question, Is 57 a Prime number or Not? However, the answer to the question is 57, not a prime number.

Apart from the above-specified ways, there are two more methods to check whether 57 is a prime number or not.

Method 1:

6(9) + 1 = 54 + 1 = 55 < 57

6(9) – 1 = 54 +-1 = 53 < 57

6(10) – 1 = 60 – 1 = 59 > 57

That means 57 cannot be expressed in the form 6n + 1 or 6n – 1, where n is a natural number. Hence, it is not a prime number.

Method 2:

To know the prime numbers greater than 40, we can use the formula below:

n² + n + 41, where n = 0, 1, 2, ….., 39

In the above formula, by substituting n = 3, we get;

(3)² + 3 + 41 = 9 + 3 + 41 = 53 < 57

Now, substituting n = 4, we get;

(4)² + 4 + 41 = 16 + 4 + 41 = 61 > 51

Thus, we can say that 61 is not a prime number.

Is 57 a Composite number?

Yes, the number 57 is composite since it has more than 2 factors and they are 1, 3, 19, and 57. That means 57 is exactly divisible by other numbers apart from 1 and the number itself. Thus, 57 goes evenly by 3 and 19 also.

57 ÷ 1 = 57 {remainder = 0}

57 ÷ 3 = 19 {remainder = 0}

57 ÷ 19 = 3 {remainder = 0}

57 ÷ 57 = 1 {remainder = 0}

Here, 1, 3, 19 and 57 are the exact divisors of 57.

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