Is 438 a prime number? What are the divisors of 438?

Is 438 a prime number?

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

For 438, the answer is: No, 438 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 438) is as follows: 1, 2, 3, 6, 73, 146, 219, 438.

To be 438 a prime number, it would have been required that 438 has only two divisors, i.e., itself and 1.

As a consequence:

  • 438 is a multiple of 1
  • 438 is a multiple of 2
  • 438 is a multiple of 3
  • 438 is a multiple of 6
  • 438 is a multiple of 73
  • 438 is a multiple of 146
  • 438 is a multiple of 219

To be 438 a prime number, it would have been required that 438 has only two divisors, i.e., itself and 1.

Is 438 a deficient number?

No, 438 is not a deficient number: to be deficient, 438 should have been such that 438 is larger than the sum of its proper divisors, i.e., the divisors of 438 without 438 itself (that is 1 + 2 + 3 + 6 + 73 + 146 + 219 = 450).

In fact, 438 is an abundant number; 438 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 73 + 146 + 219 = 450). The smallest abundant number is 12.

Parity of 438

438 is an even number, because it is evenly divisible by 2: 438 / 2 = 219.

Is 438 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 438 is about 20.928.

Thus, the square root of 438 is not an integer, and therefore 438 is not a square number.

What is the square number of 438?

The square of a number (here 438) is the result of the product of this number (438) by itself (i.e., 438 × 438); the square of 438 is sometimes called "raising 438 to the power 2", or "438 squared".

The square of 438 is 191 844 because 438 × 438 = 4382 = 191 844.

As a consequence, 438 is the square root of 191 844.

Number of digits of 438

438 is a number with 3 digits.

What are the multiples of 438?

The multiples of 438 are all integers evenly divisible by 438, that is all numbers such that the remainder of the division by 438 is zero. There are infinitely many multiples of 438. The smallest multiples of 438 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 438 too, since 0 × 438 = 0
  • 438: indeed, 438 is a multiple of itself, since 438 is evenly divisible by 438 (we have 438 / 438 = 1, so the remainder of this division is indeed zero)
  • 876: indeed, 876 = 438 × 2
  • 1 314: indeed, 1 314 = 438 × 3
  • 1 752: indeed, 1 752 = 438 × 4
  • 2 190: indeed, 2 190 = 438 × 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 438). 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 20.928). 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 438

  • Preceding numbers: …436, 437
  • Following numbers: 439, 440

Nearest numbers from 438

  • Preceding prime number: 433
  • Following prime number: 439
Find out whether some integer is a prime number