Is 921 a prime number?

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

For 921, the answer is: No, 921 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 921) is as follows: 1, 3, 307, 921.

For 921 to be a prime number, it would have been required that 921 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

921 is a multiple of 1
921 is a multiple of 3
921 is a multiple of 307

For 921 to be a prime number, it would have been required that 921 has only two divisors, i.e., itself and 1.

However, 921 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 921 = 3 x 307, where 3 and 307 are both prime numbers.

Is 921 a deficient number?

Yes, 921 is a deficient number, that is to say 921 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 921 without 921 itself (that is 1 + 3 + 307 = 311).

Parity of 921

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

Find out more:

What is an even number?

Is 921 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 921 is about 30.348.

Thus, the square root of 921 is not an integer, and therefore 921 is not a square number.

What is the square number of 921?

The square of a number (here 921) is the result of the product of this number (921) by itself (i.e., 921 × 921); the square of 921 is sometimes called "raising 921 to the power 2", or "921 squared".

The square of 921 is 848 241 because 921 × 921 = 921² = 848 241.

As a consequence, 921 is the square root of 848 241.

Number of digits of 921

921 is a number with 3 digits.

What are the multiples of 921?

The multiples of 921 are all integers evenly divisible by 921, that is all numbers such that the remainder of the division by 921 is zero. There are infinitely many multiples of 921. The smallest multiples of 921 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 921 too, since 0 × 921 = 0
921: indeed, 921 is a multiple of itself, since 921 is evenly divisible by 921 (we have 921 / 921 = 1, so the remainder of this division is indeed zero)
1 842: indeed, 1 842 = 921 × 2
2 763: indeed, 2 763 = 921 × 3
3 684: indeed, 3 684 = 921 × 4
4 605: indeed, 4 605 = 921 × 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 921). 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 30.348). 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 921

Preceding numbers: …919, 920
Following numbers: 922, 923…

Nearest numbers from 921

Preceding prime number: 919
Following prime number: 929