Is 993 a prime number?

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

For 993, the answer is: No, 993 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 993) is as follows: 1, 3, 331, 993.

For 993 to be a prime number, it would have been required that 993 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

993 is a multiple of 1
993 is a multiple of 3
993 is a multiple of 331

For 993 to be a prime number, it would have been required that 993 has only two divisors, i.e., itself and 1.

However, 993 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 993 = 3 x 331, where 3 and 331 are both prime numbers.

Is 993 a deficient number?

Yes, 993 is a deficient number, that is to say 993 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 993 without 993 itself (that is 1 + 3 + 331 = 335).

Parity of 993

993 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 993 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 993 is about 31.512.

Thus, the square root of 993 is not an integer, and therefore 993 is not a square number.

What is the square number of 993?

The square of a number (here 993) is the result of the product of this number (993) by itself (i.e., 993 × 993); the square of 993 is sometimes called "raising 993 to the power 2", or "993 squared".

The square of 993 is 986 049 because 993 × 993 = 993² = 986 049.

As a consequence, 993 is the square root of 986 049.

Number of digits of 993

993 is a number with 3 digits.

What are the multiples of 993?

The multiples of 993 are all integers evenly divisible by 993, that is all numbers such that the remainder of the division by 993 is zero. There are infinitely many multiples of 993. The smallest multiples of 993 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 993 too, since 0 × 993 = 0
993: indeed, 993 is a multiple of itself, since 993 is evenly divisible by 993 (we have 993 / 993 = 1, so the remainder of this division is indeed zero)
1 986: indeed, 1 986 = 993 × 2
2 979: indeed, 2 979 = 993 × 3
3 972: indeed, 3 972 = 993 × 4
4 965: indeed, 4 965 = 993 × 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 993). 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 31.512). 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 993

Preceding numbers: …991, 992
Following numbers: 994, 995…

Nearest numbers from 993

Preceding prime number: 991
Following prime number: 997