Is 924 a prime number?

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

For 924, the answer is: No, 924 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 924) is as follows: 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924.

For 924 to be a prime number, it would have been required that 924 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

924 is a multiple of 1
924 is a multiple of 2
924 is a multiple of 3
924 is a multiple of 4
924 is a multiple of 6
924 is a multiple of 7
924 is a multiple of 11
924 is a multiple of 12
924 is a multiple of 14
924 is a multiple of 21
924 is a multiple of 22
924 is a multiple of 28
924 is a multiple of 33
924 is a multiple of 42
924 is a multiple of 44
924 is a multiple of 66
924 is a multiple of 77
924 is a multiple of 84
924 is a multiple of 132
924 is a multiple of 154
924 is a multiple of 231
924 is a multiple of 308
924 is a multiple of 462

For 924 to be a prime number, it would have been required that 924 has only two divisors, i.e., itself and 1.

Is 924 a deficient number?

No, 924 is not a deficient number: to be deficient, 924 should have been such that 924 is larger than the sum of its proper divisors, i.e., the divisors of 924 without 924 itself (that is 1 + 2 + 3 + 4 + 6 + 7 + 11 + 12 + 14 + 21 + 22 + 28 + 33 + 42 + 44 + 66 + 77 + 84 + 132 + 154 + 231 + 308 + 462 = 1 764).

In fact, 924 is an abundant number; 924 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 7 + 11 + 12 + 14 + 21 + 22 + 28 + 33 + 42 + 44 + 66 + 77 + 84 + 132 + 154 + 231 + 308 + 462 = 1 764). The smallest abundant number is 12.

Parity of 924

924 is an even number, because it is evenly divisible by 2: 924 / 2 = 462.

Find out more:

What is an even number?

Is 924 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 924 is about 30.397.

Thus, the square root of 924 is not an integer, and therefore 924 is not a square number.

What is the square number of 924?

The square of a number (here 924) is the result of the product of this number (924) by itself (i.e., 924 × 924); the square of 924 is sometimes called "raising 924 to the power 2", or "924 squared".

The square of 924 is 853 776 because 924 × 924 = 924² = 853 776.

As a consequence, 924 is the square root of 853 776.

Number of digits of 924

924 is a number with 3 digits.

What are the multiples of 924?

The multiples of 924 are all integers evenly divisible by 924, that is all numbers such that the remainder of the division by 924 is zero. There are infinitely many multiples of 924. The smallest multiples of 924 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 924 too, since 0 × 924 = 0
924: indeed, 924 is a multiple of itself, since 924 is evenly divisible by 924 (we have 924 / 924 = 1, so the remainder of this division is indeed zero)
1 848: indeed, 1 848 = 924 × 2
2 772: indeed, 2 772 = 924 × 3
3 696: indeed, 3 696 = 924 × 4
4 620: indeed, 4 620 = 924 × 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 924). 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 30.397). 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 924

Preceding numbers: …922, 923
Following numbers: 925, 926…

Nearest numbers from 924

Preceding prime number: 919
Following prime number: 929