Is 57 A Prime Number?

Is 57 a prime number? What are the divisors of 57? To content

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 57, the answer is: No, 57 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 57) is as follows: 1, 3, 19, 57.

For 57 to be a prime number, it would have been required that 57 has only two divisors, i.e., itself and 1.

Find out more:

• What is a prime number?

As a consequence:

• 57 is a multiple of 1
• 57 is a multiple of 3
• 57 is a multiple of 19

For 57 to be a prime number, it would have been required that 57 has only two divisors, i.e., itself and 1.

However, 57 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 57 = 3 x 19, where 3 and 19 are both prime numbers.

Is 57 a deficient number?

Yes, 57 is a deficient number, that is to say 57 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 57 without 57 itself (that is 1 + 3 + 19 = 23).

57 is an odd number, because it is not evenly divisible by 2.

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• What is an even number?

A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 57 is about 7.550.

Thus, the square root of 57 is not an integer, and therefore 57 is not a square number.

The square of a number (here 57) is the result of the product of this number (57) by itself (i.e., 57 × 57); the square of 57 is sometimes called "raising 57 to the power 2", or "57 squared".

The square of 57 is 3 249 because 57 × 57 = 572 = 3 249.

As a consequence, 57 is the square root of 3 249.

57 is a number with 2 digits.

The multiples of 57 are all integers evenly divisible by 57, that is all numbers such that the remainder of the division by 57 is zero. There are infinitely many multiples of 57. The smallest multiples of 57 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 57 too, since 0 × 57 = 0
• 57: indeed, 57 is a multiple of itself, since 57 is evenly divisible by 57 (we have 57 / 57 = 1, so the remainder of this division is indeed zero)
• 114: indeed, 114 = 57 × 2
• 171: indeed, 171 = 57 × 3
• 228: indeed, 228 = 57 × 4
• 285: indeed, 285 = 57 × 5
• etc.

To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 57). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 7.550). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.

More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.

• Preceding numbers: …55, 56
• Following numbers: 58, 59…

Nearest numbers from 57

• Preceding prime number: 53
• Following prime number: 59

Find out whether some integer is a prime number

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• Home
• What is a prime number?
• A list of prime numbers
• What is an even number?
• What is a multiple of 3?
• What is a multiple of 5?
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