Is 598 a prime number?

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

For 598, the answer is: No, 598 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 598) is as follows: 1, 2, 13, 23, 26, 46, 299, 598.

For 598 to be a prime number, it would have been required that 598 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

598 is a multiple of 1
598 is a multiple of 2
598 is a multiple of 13
598 is a multiple of 23
598 is a multiple of 26
598 is a multiple of 46
598 is a multiple of 299

For 598 to be a prime number, it would have been required that 598 has only two divisors, i.e., itself and 1.

Is 598 a deficient number?

Yes, 598 is a deficient number, that is to say 598 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 598 without 598 itself (that is 1 + 2 + 13 + 23 + 26 + 46 + 299 = 410).

Parity of 598

598 is an even number, because it is evenly divisible by 2: 598 / 2 = 299.

Find out more:

What is an even number?

Is 598 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 598 is about 24.454.

Thus, the square root of 598 is not an integer, and therefore 598 is not a square number.

What is the square number of 598?

The square of a number (here 598) is the result of the product of this number (598) by itself (i.e., 598 × 598); the square of 598 is sometimes called "raising 598 to the power 2", or "598 squared".

The square of 598 is 357 604 because 598 × 598 = 598² = 357 604.

As a consequence, 598 is the square root of 357 604.

Number of digits of 598

598 is a number with 3 digits.

What are the multiples of 598?

The multiples of 598 are all integers evenly divisible by 598, that is all numbers such that the remainder of the division by 598 is zero. There are infinitely many multiples of 598. The smallest multiples of 598 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 598 too, since 0 × 598 = 0
598: indeed, 598 is a multiple of itself, since 598 is evenly divisible by 598 (we have 598 / 598 = 1, so the remainder of this division is indeed zero)
1 196: indeed, 1 196 = 598 × 2
1 794: indeed, 1 794 = 598 × 3
2 392: indeed, 2 392 = 598 × 4
2 990: indeed, 2 990 = 598 × 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 598). 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 24.454). 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 598

Preceding numbers: …596, 597
Following numbers: 599, 600…

Nearest numbers from 598

Preceding prime number: 593
Following prime number: 599