Is 441 a prime number?

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

For 441, the answer is: No, 441 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 441) is as follows: 1, 3, 7, 9, 21, 49, 63, 147, 441.

For 441 to be a prime number, it would have been required that 441 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

441 is a multiple of 1
441 is a multiple of 3
441 is a multiple of 7
441 is a multiple of 9
441 is a multiple of 21
441 is a multiple of 49
441 is a multiple of 63
441 is a multiple of 147

For 441 to be a prime number, it would have been required that 441 has only two divisors, i.e., itself and 1.

Is 441 a deficient number?

Yes, 441 is a deficient number, that is to say 441 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 441 without 441 itself (that is 1 + 3 + 7 + 9 + 21 + 49 + 63 + 147 = 300).

Parity of 441

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

Find out more:

What is an even number?

Is 441 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 441 is 21.

Therefore, the square root of 441 is an integer, and as a consequence 441 is a perfect square.

As a consequence, 21 is the square root of 441.

What is the square number of 441?

The square of a number (here 441) is the result of the product of this number (441) by itself (i.e., 441 × 441); the square of 441 is sometimes called "raising 441 to the power 2", or "441 squared".

The square of 441 is 194 481 because 441 × 441 = 441² = 194 481.

As a consequence, 441 is the square root of 194 481.

Number of digits of 441

441 is a number with 3 digits.

What are the multiples of 441?

The multiples of 441 are all integers evenly divisible by 441, that is all numbers such that the remainder of the division by 441 is zero. There are infinitely many multiples of 441. The smallest multiples of 441 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 441 too, since 0 × 441 = 0
441: indeed, 441 is a multiple of itself, since 441 is evenly divisible by 441 (we have 441 / 441 = 1, so the remainder of this division is indeed zero)
882: indeed, 882 = 441 × 2
1 323: indeed, 1 323 = 441 × 3
1 764: indeed, 1 764 = 441 × 4
2 205: indeed, 2 205 = 441 × 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 441). 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 21). 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 441

Preceding numbers: …439, 440
Following numbers: 442, 443…

Nearest numbers from 441

Preceding prime number: 439
Following prime number: 443