Is 426 a prime number?

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

For 426, the answer is: No, 426 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 426) is as follows: 1, 2, 3, 6, 71, 142, 213, 426.

For 426 to be a prime number, it would have been required that 426 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

426 is a multiple of 1
426 is a multiple of 2
426 is a multiple of 3
426 is a multiple of 6
426 is a multiple of 71
426 is a multiple of 142
426 is a multiple of 213

For 426 to be a prime number, it would have been required that 426 has only two divisors, i.e., itself and 1.

Is 426 a deficient number?

No, 426 is not a deficient number: to be deficient, 426 should have been such that 426 is larger than the sum of its proper divisors, i.e., the divisors of 426 without 426 itself (that is 1 + 2 + 3 + 6 + 71 + 142 + 213 = 438).

In fact, 426 is an abundant number; 426 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 71 + 142 + 213 = 438). The smallest abundant number is 12.

Parity of 426

426 is an even number, because it is evenly divisible by 2: 426 / 2 = 213.

Find out more:

What is an even number?

Is 426 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 426 is about 20.640.

Thus, the square root of 426 is not an integer, and therefore 426 is not a square number.

What is the square number of 426?

The square of a number (here 426) is the result of the product of this number (426) by itself (i.e., 426 × 426); the square of 426 is sometimes called "raising 426 to the power 2", or "426 squared".

The square of 426 is 181 476 because 426 × 426 = 426² = 181 476.

As a consequence, 426 is the square root of 181 476.

Number of digits of 426

426 is a number with 3 digits.

What are the multiples of 426?

The multiples of 426 are all integers evenly divisible by 426, that is all numbers such that the remainder of the division by 426 is zero. There are infinitely many multiples of 426. The smallest multiples of 426 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 426 too, since 0 × 426 = 0
426: indeed, 426 is a multiple of itself, since 426 is evenly divisible by 426 (we have 426 / 426 = 1, so the remainder of this division is indeed zero)
852: indeed, 852 = 426 × 2
1 278: indeed, 1 278 = 426 × 3
1 704: indeed, 1 704 = 426 × 4
2 130: indeed, 2 130 = 426 × 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 426). 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 20.640). 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 426

Preceding numbers: …424, 425
Following numbers: 427, 428…

Nearest numbers from 426

Preceding prime number: 421
Following prime number: 431