Is 437 a prime number? What are the divisors of 437?

Is 437 a prime number?

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

For 437, the answer is: No, 437 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 437) is as follows: 1, 19, 23, 437.

To be 437 a prime number, it would have been required that 437 has only two divisors, i.e., itself and 1.

As a consequence:

  • 437 is a multiple of 1
  • 437 is a multiple of 19
  • 437 is a multiple of 23

To be 437 a prime number, it would have been required that 437 has only two divisors, i.e., itself and 1.

However, 437 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 437 = 19 x 23, where 19 and 23 are both prime numbers.

Is 437 a deficient number?

Yes, 437 is a deficient number, that is to say 437 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 437 without 437 itself (that is 1 + 19 + 23 = 43).

Parity of 437

437 is an odd number, because it is not evenly divisible by 2.

Is 437 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 437 is about 20.905.

Thus, the square root of 437 is not an integer, and therefore 437 is not a square number.

What is the square number of 437?

The square of a number (here 437) is the result of the product of this number (437) by itself (i.e., 437 × 437); the square of 437 is sometimes called "raising 437 to the power 2", or "437 squared".

The square of 437 is 190 969 because 437 × 437 = 4372 = 190 969.

As a consequence, 437 is the square root of 190 969.

Number of digits of 437

437 is a number with 3 digits.

What are the multiples of 437?

The multiples of 437 are all integers evenly divisible by 437, that is all numbers such that the remainder of the division by 437 is zero. There are infinitely many multiples of 437. The smallest multiples of 437 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 437 too, since 0 × 437 = 0
  • 437: indeed, 437 is a multiple of itself, since 437 is evenly divisible by 437 (we have 437 / 437 = 1, so the remainder of this division is indeed zero)
  • 874: indeed, 874 = 437 × 2
  • 1 311: indeed, 1 311 = 437 × 3
  • 1 748: indeed, 1 748 = 437 × 4
  • 2 185: indeed, 2 185 = 437 × 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 437). 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 20.905). 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 437

  • Preceding numbers: …435, 436
  • Following numbers: 438, 439

Nearest numbers from 437

  • Preceding prime number: 433
  • Following prime number: 439
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