Is 984 a prime number?

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

For 984, the answer is: No, 984 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 984) is as follows: 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984.

For 984 to be a prime number, it would have been required that 984 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

984 is a multiple of 1
984 is a multiple of 2
984 is a multiple of 3
984 is a multiple of 4
984 is a multiple of 6
984 is a multiple of 8
984 is a multiple of 12
984 is a multiple of 24
984 is a multiple of 41
984 is a multiple of 82
984 is a multiple of 123
984 is a multiple of 164
984 is a multiple of 246
984 is a multiple of 328
984 is a multiple of 492

For 984 to be a prime number, it would have been required that 984 has only two divisors, i.e., itself and 1.

Is 984 a deficient number?

No, 984 is not a deficient number: to be deficient, 984 should have been such that 984 is larger than the sum of its proper divisors, i.e., the divisors of 984 without 984 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 + 41 + 82 + 123 + 164 + 246 + 328 + 492 = 1 536).

In fact, 984 is an abundant number; 984 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 + 41 + 82 + 123 + 164 + 246 + 328 + 492 = 1 536). The smallest abundant number is 12.

Parity of 984

984 is an even number, because it is evenly divisible by 2: 984 / 2 = 492.

Find out more:

What is an even number?

Is 984 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 984 is about 31.369.

Thus, the square root of 984 is not an integer, and therefore 984 is not a square number.

What is the square number of 984?

The square of a number (here 984) is the result of the product of this number (984) by itself (i.e., 984 × 984); the square of 984 is sometimes called "raising 984 to the power 2", or "984 squared".

The square of 984 is 968 256 because 984 × 984 = 984² = 968 256.

As a consequence, 984 is the square root of 968 256.

Number of digits of 984

984 is a number with 3 digits.

What are the multiples of 984?

The multiples of 984 are all integers evenly divisible by 984, that is all numbers such that the remainder of the division by 984 is zero. There are infinitely many multiples of 984. The smallest multiples of 984 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 984 too, since 0 × 984 = 0
984: indeed, 984 is a multiple of itself, since 984 is evenly divisible by 984 (we have 984 / 984 = 1, so the remainder of this division is indeed zero)
1 968: indeed, 1 968 = 984 × 2
2 952: indeed, 2 952 = 984 × 3
3 936: indeed, 3 936 = 984 × 4
4 920: indeed, 4 920 = 984 × 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 984). 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 31.369). 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 984

Preceding numbers: …982, 983
Following numbers: 985, 986…

Nearest numbers from 984

Preceding prime number: 983
Following prime number: 991