Is 448 a prime number?

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

For 448, the answer is: No, 448 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 448) is as follows: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448.

For 448 to be a prime number, it would have been required that 448 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

448 is a multiple of 1
448 is a multiple of 2
448 is a multiple of 4
448 is a multiple of 7
448 is a multiple of 8
448 is a multiple of 14
448 is a multiple of 16
448 is a multiple of 28
448 is a multiple of 32
448 is a multiple of 56
448 is a multiple of 64
448 is a multiple of 112
448 is a multiple of 224

For 448 to be a prime number, it would have been required that 448 has only two divisors, i.e., itself and 1.

Is 448 a deficient number?

No, 448 is not a deficient number: to be deficient, 448 should have been such that 448 is larger than the sum of its proper divisors, i.e., the divisors of 448 without 448 itself (that is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 32 + 56 + 64 + 112 + 224 = 568).

In fact, 448 is an abundant number; 448 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 32 + 56 + 64 + 112 + 224 = 568). The smallest abundant number is 12.

Parity of 448

448 is an even number, because it is evenly divisible by 2: 448 / 2 = 224.

Find out more:

What is an even number?

Is 448 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 448 is about 21.166.

Thus, the square root of 448 is not an integer, and therefore 448 is not a square number.

What is the square number of 448?

The square of a number (here 448) is the result of the product of this number (448) by itself (i.e., 448 × 448); the square of 448 is sometimes called "raising 448 to the power 2", or "448 squared".

The square of 448 is 200 704 because 448 × 448 = 448² = 200 704.

As a consequence, 448 is the square root of 200 704.

Number of digits of 448

448 is a number with 3 digits.

What are the multiples of 448?

The multiples of 448 are all integers evenly divisible by 448, that is all numbers such that the remainder of the division by 448 is zero. There are infinitely many multiples of 448. The smallest multiples of 448 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 448 too, since 0 × 448 = 0
448: indeed, 448 is a multiple of itself, since 448 is evenly divisible by 448 (we have 448 / 448 = 1, so the remainder of this division is indeed zero)
896: indeed, 896 = 448 × 2
1 344: indeed, 1 344 = 448 × 3
1 792: indeed, 1 792 = 448 × 4
2 240: indeed, 2 240 = 448 × 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 448). 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 21.166). 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 448

Preceding numbers: …446, 447
Following numbers: 449, 450…

Nearest numbers from 448

Preceding prime number: 443
Following prime number: 449