Is 440 a prime number?

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

For 440, the answer is: No, 440 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 440) is as follows: 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440.

For 440 to be a prime number, it would have been required that 440 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 440 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 440 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

440 is a multiple of 1
440 is a multiple of 2
440 is a multiple of 4
440 is a multiple of 5
440 is a multiple of 8
440 is a multiple of 10
440 is a multiple of 11
440 is a multiple of 20
440 is a multiple of 22
440 is a multiple of 40
440 is a multiple of 44
440 is a multiple of 55
440 is a multiple of 88
440 is a multiple of 110
440 is a multiple of 220

For 440 to be a prime number, it would have been required that 440 has only two divisors, i.e., itself and 1.

Is 440 a deficient number?

No, 440 is not a deficient number: to be deficient, 440 should have been such that 440 is larger than the sum of its proper divisors, i.e., the divisors of 440 without 440 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 11 + 20 + 22 + 40 + 44 + 55 + 88 + 110 + 220 = 640).

In fact, 440 is an abundant number; 440 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 11 + 20 + 22 + 40 + 44 + 55 + 88 + 110 + 220 = 640). The smallest abundant number is 12.

Parity of 440

440 is an even number, because it is evenly divisible by 2: 440 / 2 = 220.

Find out more:

What is an even number?

Is 440 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 440 is about 20.976.

Thus, the square root of 440 is not an integer, and therefore 440 is not a square number.

What is the square number of 440?

The square of a number (here 440) is the result of the product of this number (440) by itself (i.e., 440 × 440); the square of 440 is sometimes called "raising 440 to the power 2", or "440 squared".

The square of 440 is 193 600 because 440 × 440 = 440² = 193 600.

As a consequence, 440 is the square root of 193 600.

Number of digits of 440

440 is a number with 3 digits.

What are the multiples of 440?

The multiples of 440 are all integers evenly divisible by 440, that is all numbers such that the remainder of the division by 440 is zero. There are infinitely many multiples of 440. The smallest multiples of 440 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 440 too, since 0 × 440 = 0
440: indeed, 440 is a multiple of itself, since 440 is evenly divisible by 440 (we have 440 / 440 = 1, so the remainder of this division is indeed zero)
880: indeed, 880 = 440 × 2
1 320: indeed, 1 320 = 440 × 3
1 760: indeed, 1 760 = 440 × 4
2 200: indeed, 2 200 = 440 × 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 440). 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 20.976). 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 440

Preceding numbers: …438, 439
Following numbers: 441, 442…

Nearest numbers from 440

Preceding prime number: 439
Following prime number: 443