Is 442 a prime number? What are the divisors of 442?

Is 442 a prime number?

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

For 442, the answer is: No, 442 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 442) is as follows: 1, 2, 13, 17, 26, 34, 221, 442.

To be 442 a prime number, it would have been required that 442 has only two divisors, i.e., itself and 1.

As a consequence:

  • 442 is a multiple of 1
  • 442 is a multiple of 2
  • 442 is a multiple of 13
  • 442 is a multiple of 17
  • 442 is a multiple of 26
  • 442 is a multiple of 34
  • 442 is a multiple of 221

To be 442 a prime number, it would have been required that 442 has only two divisors, i.e., itself and 1.

Is 442 a deficient number?

Yes, 442 is a deficient number, that is to say 442 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 442 without 442 itself (that is 1 + 2 + 13 + 17 + 26 + 34 + 221 = 314).

Parity of 442

442 is an even number, because it is evenly divisible by 2: 442 / 2 = 221.

Is 442 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 442 is about 21.024.

Thus, the square root of 442 is not an integer, and therefore 442 is not a square number.

What is the square number of 442?

The square of a number (here 442) is the result of the product of this number (442) by itself (i.e., 442 × 442); the square of 442 is sometimes called "raising 442 to the power 2", or "442 squared".

The square of 442 is 195 364 because 442 × 442 = 4422 = 195 364.

As a consequence, 442 is the square root of 195 364.

Number of digits of 442

442 is a number with 3 digits.

What are the multiples of 442?

The multiples of 442 are all integers evenly divisible by 442, that is all numbers such that the remainder of the division by 442 is zero. There are infinitely many multiples of 442. The smallest multiples of 442 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 442 too, since 0 × 442 = 0
  • 442: indeed, 442 is a multiple of itself, since 442 is evenly divisible by 442 (we have 442 / 442 = 1, so the remainder of this division is indeed zero)
  • 884: indeed, 884 = 442 × 2
  • 1 326: indeed, 1 326 = 442 × 3
  • 1 768: indeed, 1 768 = 442 × 4
  • 2 210: indeed, 2 210 = 442 × 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 442). 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 21.024). 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 442

  • Preceding numbers: …440, 441
  • Following numbers: 443, 444

Nearest numbers from 442

  • Preceding prime number: 439
  • Following prime number: 443
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