Is 981 a prime number?

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

For 981, the answer is: No, 981 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 981) is as follows: 1, 3, 9, 109, 327, 981.

For 981 to be a prime number, it would have been required that 981 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

981 is a multiple of 1
981 is a multiple of 3
981 is a multiple of 9
981 is a multiple of 109
981 is a multiple of 327

For 981 to be a prime number, it would have been required that 981 has only two divisors, i.e., itself and 1.

Is 981 a deficient number?

Yes, 981 is a deficient number, that is to say 981 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 981 without 981 itself (that is 1 + 3 + 9 + 109 + 327 = 449).

Parity of 981

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

Find out more:

What is an even number?

Is 981 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 981 is about 31.321.

Thus, the square root of 981 is not an integer, and therefore 981 is not a square number.

What is the square number of 981?

The square of a number (here 981) is the result of the product of this number (981) by itself (i.e., 981 × 981); the square of 981 is sometimes called "raising 981 to the power 2", or "981 squared".

The square of 981 is 962 361 because 981 × 981 = 981² = 962 361.

As a consequence, 981 is the square root of 962 361.

Number of digits of 981

981 is a number with 3 digits.

What are the multiples of 981?

The multiples of 981 are all integers evenly divisible by 981, that is all numbers such that the remainder of the division by 981 is zero. There are infinitely many multiples of 981. The smallest multiples of 981 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 981 too, since 0 × 981 = 0
981: indeed, 981 is a multiple of itself, since 981 is evenly divisible by 981 (we have 981 / 981 = 1, so the remainder of this division is indeed zero)
1 962: indeed, 1 962 = 981 × 2
2 943: indeed, 2 943 = 981 × 3
3 924: indeed, 3 924 = 981 × 4
4 905: indeed, 4 905 = 981 × 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 981). 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 31.321). 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 981

Preceding numbers: …979, 980
Following numbers: 982, 983…

Nearest numbers from 981

Preceding prime number: 977
Following prime number: 983