Is 527 a prime number?

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

For 527, the answer is: No, 527 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 527) is as follows: 1, 17, 31, 527.

For 527 to be a prime number, it would have been required that 527 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

527 is a multiple of 1
527 is a multiple of 17
527 is a multiple of 31

For 527 to be a prime number, it would have been required that 527 has only two divisors, i.e., itself and 1.

However, 527 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 527 = 17 x 31, where 17 and 31 are both prime numbers.

Is 527 a deficient number?

Yes, 527 is a deficient number, that is to say 527 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 527 without 527 itself (that is 1 + 17 + 31 = 49).

Parity of 527

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

Find out more:

What is an even number?

Is 527 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 527 is about 22.956.

Thus, the square root of 527 is not an integer, and therefore 527 is not a square number.

What is the square number of 527?

The square of a number (here 527) is the result of the product of this number (527) by itself (i.e., 527 × 527); the square of 527 is sometimes called "raising 527 to the power 2", or "527 squared".

The square of 527 is 277 729 because 527 × 527 = 527² = 277 729.

As a consequence, 527 is the square root of 277 729.

Number of digits of 527

527 is a number with 3 digits.

What are the multiples of 527?

The multiples of 527 are all integers evenly divisible by 527, that is all numbers such that the remainder of the division by 527 is zero. There are infinitely many multiples of 527. The smallest multiples of 527 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 527 too, since 0 × 527 = 0
527: indeed, 527 is a multiple of itself, since 527 is evenly divisible by 527 (we have 527 / 527 = 1, so the remainder of this division is indeed zero)
1 054: indeed, 1 054 = 527 × 2
1 581: indeed, 1 581 = 527 × 3
2 108: indeed, 2 108 = 527 × 4
2 635: indeed, 2 635 = 527 × 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 527). 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 22.956). 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 527

Preceding numbers: …525, 526
Following numbers: 528, 529…

Nearest numbers from 527

Preceding prime number: 523
Following prime number: 541