Is 624 a prime number?

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

For 624, the answer is: No, 624 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 624) is as follows: 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624.

For 624 to be a prime number, it would have been required that 624 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

624 is a multiple of 1
624 is a multiple of 2
624 is a multiple of 3
624 is a multiple of 4
624 is a multiple of 6
624 is a multiple of 8
624 is a multiple of 12
624 is a multiple of 13
624 is a multiple of 16
624 is a multiple of 24
624 is a multiple of 26
624 is a multiple of 39
624 is a multiple of 48
624 is a multiple of 52
624 is a multiple of 78
624 is a multiple of 104
624 is a multiple of 156
624 is a multiple of 208
624 is a multiple of 312

For 624 to be a prime number, it would have been required that 624 has only two divisors, i.e., itself and 1.

Is 624 a deficient number?

No, 624 is not a deficient number: to be deficient, 624 should have been such that 624 is larger than the sum of its proper divisors, i.e., the divisors of 624 without 624 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 16 + 24 + 26 + 39 + 48 + 52 + 78 + 104 + 156 + 208 + 312 = 1 112).

In fact, 624 is an abundant number; 624 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 16 + 24 + 26 + 39 + 48 + 52 + 78 + 104 + 156 + 208 + 312 = 1 112). The smallest abundant number is 12.

Parity of 624

624 is an even number, because it is evenly divisible by 2: 624 / 2 = 312.

Find out more:

What is an even number?

Is 624 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 624 is about 24.980.

Thus, the square root of 624 is not an integer, and therefore 624 is not a square number.

What is the square number of 624?

The square of a number (here 624) is the result of the product of this number (624) by itself (i.e., 624 × 624); the square of 624 is sometimes called "raising 624 to the power 2", or "624 squared".

The square of 624 is 389 376 because 624 × 624 = 624² = 389 376.

As a consequence, 624 is the square root of 389 376.

Number of digits of 624

624 is a number with 3 digits.

What are the multiples of 624?

The multiples of 624 are all integers evenly divisible by 624, that is all numbers such that the remainder of the division by 624 is zero. There are infinitely many multiples of 624. The smallest multiples of 624 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 624 too, since 0 × 624 = 0
624: indeed, 624 is a multiple of itself, since 624 is evenly divisible by 624 (we have 624 / 624 = 1, so the remainder of this division is indeed zero)
1 248: indeed, 1 248 = 624 × 2
1 872: indeed, 1 872 = 624 × 3
2 496: indeed, 2 496 = 624 × 4
3 120: indeed, 3 120 = 624 × 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 624). 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 24.980). 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 624

Preceding numbers: …622, 623
Following numbers: 625, 626…

Nearest numbers from 624

Preceding prime number: 619
Following prime number: 631