Is 529 a prime number? What are the divisors of 529?

Is 529 a prime number?

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

For 529, the answer is: No, 529 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 529) is as follows: 1, 23, 529.

To be 529 a prime number, it would have been required that 529 has only two divisors, i.e., itself and 1.

As a consequence:

  • 529 is a multiple of 1
  • 529 is a multiple of 23

To be 529 a prime number, it would have been required that 529 has only two divisors, i.e., itself and 1.

However, 529 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 529 = 23 x 23, where 23 is a prime number.

Is 529 a deficient number?

Yes, 529 is a deficient number, that is to say 529 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 529 without 529 itself (that is 1 + 23 = 24).

Parity of 529

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

Is 529 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 529 is 23.

Therefore, the square root of 529 is an integer, and as a consequence 529 is a perfect square.

As a consequence, 23 is the square root of 529.

What is the square number of 529?

The square of a number (here 529) is the result of the product of this number (529) by itself (i.e., 529 × 529); the square of 529 is sometimes called "raising 529 to the power 2", or "529 squared".

The square of 529 is 279 841 because 529 × 529 = 5292 = 279 841.

As a consequence, 529 is the square root of 279 841.

Number of digits of 529

529 is a number with 3 digits.

What are the multiples of 529?

The multiples of 529 are all integers evenly divisible by 529, that is all numbers such that the remainder of the division by 529 is zero. There are infinitely many multiples of 529. The smallest multiples of 529 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 529 too, since 0 × 529 = 0
  • 529: indeed, 529 is a multiple of itself, since 529 is evenly divisible by 529 (we have 529 / 529 = 1, so the remainder of this division is indeed zero)
  • 1 058: indeed, 1 058 = 529 × 2
  • 1 587: indeed, 1 587 = 529 × 3
  • 2 116: indeed, 2 116 = 529 × 4
  • 2 645: indeed, 2 645 = 529 × 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 529). 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 23). 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 529

  • Preceding numbers: …527, 528
  • Following numbers: 530, 531

Nearest numbers from 529

  • Preceding prime number: 523
  • Following prime number: 541
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