Is 428 a prime number?

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

For 428, the answer is: No, 428 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 428) is as follows: 1, 2, 4, 107, 214, 428.

For 428 to be a prime number, it would have been required that 428 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

428 is a multiple of 1
428 is a multiple of 2
428 is a multiple of 4
428 is a multiple of 107
428 is a multiple of 214

For 428 to be a prime number, it would have been required that 428 has only two divisors, i.e., itself and 1.

Is 428 a deficient number?

Yes, 428 is a deficient number, that is to say 428 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 428 without 428 itself (that is 1 + 2 + 4 + 107 + 214 = 328).

Parity of 428

428 is an even number, because it is evenly divisible by 2: 428 / 2 = 214.

Find out more:

What is an even number?

Is 428 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 428 is about 20.688.

Thus, the square root of 428 is not an integer, and therefore 428 is not a square number.

What is the square number of 428?

The square of a number (here 428) is the result of the product of this number (428) by itself (i.e., 428 × 428); the square of 428 is sometimes called "raising 428 to the power 2", or "428 squared".

The square of 428 is 183 184 because 428 × 428 = 428² = 183 184.

As a consequence, 428 is the square root of 183 184.

Number of digits of 428

428 is a number with 3 digits.

What are the multiples of 428?

The multiples of 428 are all integers evenly divisible by 428, that is all numbers such that the remainder of the division by 428 is zero. There are infinitely many multiples of 428. The smallest multiples of 428 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 428 too, since 0 × 428 = 0
428: indeed, 428 is a multiple of itself, since 428 is evenly divisible by 428 (we have 428 / 428 = 1, so the remainder of this division is indeed zero)
856: indeed, 856 = 428 × 2
1 284: indeed, 1 284 = 428 × 3
1 712: indeed, 1 712 = 428 × 4
2 140: indeed, 2 140 = 428 × 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 428). 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 20.688). 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 428

Preceding numbers: …426, 427
Following numbers: 429, 430…

Nearest numbers from 428

Preceding prime number: 421
Following prime number: 431