Is 528 a prime number?

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

For 528, the answer is: No, 528 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 528) is as follows: 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528.

For 528 to be a prime number, it would have been required that 528 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

528 is a multiple of 1
528 is a multiple of 2
528 is a multiple of 3
528 is a multiple of 4
528 is a multiple of 6
528 is a multiple of 8
528 is a multiple of 11
528 is a multiple of 12
528 is a multiple of 16
528 is a multiple of 22
528 is a multiple of 24
528 is a multiple of 33
528 is a multiple of 44
528 is a multiple of 48
528 is a multiple of 66
528 is a multiple of 88
528 is a multiple of 132
528 is a multiple of 176
528 is a multiple of 264

For 528 to be a prime number, it would have been required that 528 has only two divisors, i.e., itself and 1.

Is 528 a deficient number?

No, 528 is not a deficient number: to be deficient, 528 should have been such that 528 is larger than the sum of its proper divisors, i.e., the divisors of 528 without 528 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 11 + 12 + 16 + 22 + 24 + 33 + 44 + 48 + 66 + 88 + 132 + 176 + 264 = 960).

In fact, 528 is an abundant number; 528 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 11 + 12 + 16 + 22 + 24 + 33 + 44 + 48 + 66 + 88 + 132 + 176 + 264 = 960). The smallest abundant number is 12.

Parity of 528

528 is an even number, because it is evenly divisible by 2: 528 / 2 = 264.

Find out more:

What is an even number?

Is 528 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 528 is about 22.978.

Thus, the square root of 528 is not an integer, and therefore 528 is not a square number.

What is the square number of 528?

The square of a number (here 528) is the result of the product of this number (528) by itself (i.e., 528 × 528); the square of 528 is sometimes called "raising 528 to the power 2", or "528 squared".

The square of 528 is 278 784 because 528 × 528 = 528² = 278 784.

As a consequence, 528 is the square root of 278 784.

Number of digits of 528

528 is a number with 3 digits.

What are the multiples of 528?

The multiples of 528 are all integers evenly divisible by 528, that is all numbers such that the remainder of the division by 528 is zero. There are infinitely many multiples of 528. The smallest multiples of 528 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 528 too, since 0 × 528 = 0
528: indeed, 528 is a multiple of itself, since 528 is evenly divisible by 528 (we have 528 / 528 = 1, so the remainder of this division is indeed zero)
1 056: indeed, 1 056 = 528 × 2
1 584: indeed, 1 584 = 528 × 3
2 112: indeed, 2 112 = 528 × 4
2 640: indeed, 2 640 = 528 × 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 528). 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 22.978). 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 528

Preceding numbers: …526, 527
Following numbers: 529, 530…

Nearest numbers from 528

Preceding prime number: 523
Following prime number: 541