Is 998 a prime number?

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

For 998, the answer is: No, 998 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 998) is as follows: 1, 2, 499, 998.

For 998 to be a prime number, it would have been required that 998 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

998 is a multiple of 1
998 is a multiple of 2
998 is a multiple of 499

For 998 to be a prime number, it would have been required that 998 has only two divisors, i.e., itself and 1.

However, 998 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 998 = 2 x 499, where 2 and 499 are both prime numbers.

Is 998 a deficient number?

Yes, 998 is a deficient number, that is to say 998 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 998 without 998 itself (that is 1 + 2 + 499 = 502).

Parity of 998

998 is an even number, because it is evenly divisible by 2: 998 / 2 = 499.

Find out more:

What is an even number?

Is 998 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 998 is about 31.591.

Thus, the square root of 998 is not an integer, and therefore 998 is not a square number.

What is the square number of 998?

The square of a number (here 998) is the result of the product of this number (998) by itself (i.e., 998 × 998); the square of 998 is sometimes called "raising 998 to the power 2", or "998 squared".

The square of 998 is 996 004 because 998 × 998 = 998² = 996 004.

As a consequence, 998 is the square root of 996 004.

Number of digits of 998

998 is a number with 3 digits.

What are the multiples of 998?

The multiples of 998 are all integers evenly divisible by 998, that is all numbers such that the remainder of the division by 998 is zero. There are infinitely many multiples of 998. The smallest multiples of 998 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 998 too, since 0 × 998 = 0
998: indeed, 998 is a multiple of itself, since 998 is evenly divisible by 998 (we have 998 / 998 = 1, so the remainder of this division is indeed zero)
1 996: indeed, 1 996 = 998 × 2
2 994: indeed, 2 994 = 998 × 3
3 992: indeed, 3 992 = 998 × 4
4 990: indeed, 4 990 = 998 × 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 998). 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 31.591). 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 998

Preceding numbers: …996, 997
Following numbers: 999, 1 000…

Nearest numbers from 998

Preceding prime number: 997
Following prime number: 1 009