Is 51 a prime number? What are the divisors of 51?

Is 51 a prime number?

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

For 51, the answer is: No, 51 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 51) is as follows: 1, 3, 17, 51.

To be 51 a prime number, it would have been required that 51 has only two divisors, i.e., itself and 1.

As a consequence:

  • 51 is a multiple of 1
  • 51 is a multiple of 3
  • 51 is a multiple of 17

To be 51 a prime number, it would have been required that 51 has only two divisors, i.e., itself and 1.

However, 51 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 51 = 3 x 17, where 3 and 17 are both prime numbers.

Is 51 a deficient number?

Yes, 51 is a deficient number, that is to say 51 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 51 without 51 itself (that is 1 + 3 + 17 = 21).

Parity of 51

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

Is 51 a perfect square 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 51 is about 7.141.

Thus, the square root of 51 is not an integer, and therefore 51 is not a square number.

What is the square number of 51?

The square of a number (here 51) is the result of the product of this number (51) by itself (i.e., 51 × 51); the square of 51 is sometimes called "raising 51 to the power 2", or "51 squared".

The square of 51 is 2 601 because 51 × 51 = 512 = 2 601.

As a consequence, 51 is the square root of 2 601.

Number of digits of 51

51 is a number with 2 digits.

What are the multiples of 51?

The multiples of 51 are all integers evenly divisible by 51, that is all numbers such that the remainder of the division by 51 is zero. There are infinitely many multiples of 51. The smallest multiples of 51 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 51 too, since 0 × 51 = 0
  • 51: indeed, 51 is a multiple of itself, since 51 is evenly divisible by 51 (we have 51 / 51 = 1, so the remainder of this division is indeed zero)
  • 102: indeed, 102 = 51 × 2
  • 153: indeed, 153 = 51 × 3
  • 204: indeed, 204 = 51 × 4
  • 255: indeed, 255 = 51 × 5
  • etc.

How to determine whether an integer is a prime number?

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 51). 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 7.141). 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.

Numbers near 51

  • Preceding numbers: …49, 50
  • Following numbers: 52, 53

Nearest numbers from 51

  • Preceding prime number: 47
  • Following prime number: 53
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