Is 24 a prime number? What are the divisors of 24?

Is 24 a prime number?

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

For 24, the answer is: No, 24 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 24) is as follows: 1, 2, 3, 4, 6, 8, 12, 24.

To be 24 a prime number, it would have been required that 24 has only two divisors, i.e., itself and 1.

As a consequence:

  • 24 is a multiple of 1
  • 24 is a multiple of 2
  • 24 is a multiple of 3
  • 24 is a multiple of 4
  • 24 is a multiple of 6
  • 24 is a multiple of 8
  • 24 is a multiple of 12

To be 24 a prime number, it would have been required that 24 has only two divisors, i.e., itself and 1.

Is 24 a deficient number?

No, 24 is not a deficient number: to be deficient, 24 should have been such that 24 is larger than the sum of its proper divisors, i.e., the divisors of 24 without 24 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 = 36).

In fact, 24 is an abundant number; 24 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 = 36). The smallest abundant number is 12.

Parity of 24

24 is an even number, because it is evenly divisible by 2: 24 / 2 = 12.

Is 24 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 24 is about 4.899.

Thus, the square root of 24 is not an integer, and therefore 24 is not a square number.

What is the square number of 24?

The square of a number (here 24) is the result of the product of this number (24) by itself (i.e., 24 × 24); the square of 24 is sometimes called "raising 24 to the power 2", or "24 squared".

The square of 24 is 576 because 24 × 24 = 242 = 576.

As a consequence, 24 is the square root of 576.

Number of digits of 24

24 is a number with 2 digits.

What are the multiples of 24?

The multiples of 24 are all integers evenly divisible by 24, that is all numbers such that the remainder of the division by 24 is zero. There are infinitely many multiples of 24. The smallest multiples of 24 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 24 too, since 0 × 24 = 0
  • 24: indeed, 24 is a multiple of itself, since 24 is evenly divisible by 24 (we have 24 / 24 = 1, so the remainder of this division is indeed zero)
  • 48: indeed, 48 = 24 × 2
  • 72: indeed, 72 = 24 × 3
  • 96: indeed, 96 = 24 × 4
  • 120: indeed, 120 = 24 × 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 24). 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 4.899). 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 24

  • Preceding numbers: …22, 23
  • Following numbers: 25, 26

Nearest numbers from 24

  • Preceding prime number: 23
  • Following prime number: 29
Find out whether some integer is a prime number