Is 52 a prime number? What are the divisors of 52?

Is 52 a prime number?

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

For 52, the answer is: No, 52 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 52) is as follows: 1, 2, 4, 13, 26, 52.

To be 52 a prime number, it would have been required that 52 has only two divisors, i.e., itself and 1.

As a consequence:

  • 52 is a multiple of 1
  • 52 is a multiple of 2
  • 52 is a multiple of 4
  • 52 is a multiple of 13
  • 52 is a multiple of 26

To be 52 a prime number, it would have been required that 52 has only two divisors, i.e., itself and 1.

Is 52 a deficient number?

Yes, 52 is a deficient number, that is to say 52 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 52 without 52 itself (that is 1 + 2 + 4 + 13 + 26 = 46).

Parity of 52

52 is an even number, because it is evenly divisible by 2: 52 / 2 = 26.

Is 52 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 52 is about 7.211.

Thus, the square root of 52 is not an integer, and therefore 52 is not a square number.

What is the square number of 52?

The square of a number (here 52) is the result of the product of this number (52) by itself (i.e., 52 × 52); the square of 52 is sometimes called "raising 52 to the power 2", or "52 squared".

The square of 52 is 2 704 because 52 × 52 = 522 = 2 704.

As a consequence, 52 is the square root of 2 704.

Number of digits of 52

52 is a number with 2 digits.

What are the multiples of 52?

The multiples of 52 are all integers evenly divisible by 52, that is all numbers such that the remainder of the division by 52 is zero. There are infinitely many multiples of 52. The smallest multiples of 52 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 52 too, since 0 × 52 = 0
  • 52: indeed, 52 is a multiple of itself, since 52 is evenly divisible by 52 (we have 52 / 52 = 1, so the remainder of this division is indeed zero)
  • 104: indeed, 104 = 52 × 2
  • 156: indeed, 156 = 52 × 3
  • 208: indeed, 208 = 52 × 4
  • 260: indeed, 260 = 52 × 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 52). 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 7.211). 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 52

  • Preceding numbers: …50, 51
  • Following numbers: 53, 54

Nearest numbers from 52

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