Is 920 a prime number?

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

For 920, the answer is: No, 920 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 920) is as follows: 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920.

For 920 to be a prime number, it would have been required that 920 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 920 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 920 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

920 is a multiple of 1
920 is a multiple of 2
920 is a multiple of 4
920 is a multiple of 5
920 is a multiple of 8
920 is a multiple of 10
920 is a multiple of 20
920 is a multiple of 23
920 is a multiple of 40
920 is a multiple of 46
920 is a multiple of 92
920 is a multiple of 115
920 is a multiple of 184
920 is a multiple of 230
920 is a multiple of 460

For 920 to be a prime number, it would have been required that 920 has only two divisors, i.e., itself and 1.

Is 920 a deficient number?

No, 920 is not a deficient number: to be deficient, 920 should have been such that 920 is larger than the sum of its proper divisors, i.e., the divisors of 920 without 920 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 + 23 + 40 + 46 + 92 + 115 + 184 + 230 + 460 = 1 240).

In fact, 920 is an abundant number; 920 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 + 23 + 40 + 46 + 92 + 115 + 184 + 230 + 460 = 1 240). The smallest abundant number is 12.

Parity of 920

920 is an even number, because it is evenly divisible by 2: 920 / 2 = 460.

Find out more:

What is an even number?

Is 920 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 920 is about 30.332.

Thus, the square root of 920 is not an integer, and therefore 920 is not a square number.

What is the square number of 920?

The square of a number (here 920) is the result of the product of this number (920) by itself (i.e., 920 × 920); the square of 920 is sometimes called "raising 920 to the power 2", or "920 squared".

The square of 920 is 846 400 because 920 × 920 = 920² = 846 400.

As a consequence, 920 is the square root of 846 400.

Number of digits of 920

920 is a number with 3 digits.

What are the multiples of 920?

The multiples of 920 are all integers evenly divisible by 920, that is all numbers such that the remainder of the division by 920 is zero. There are infinitely many multiples of 920. The smallest multiples of 920 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 920 too, since 0 × 920 = 0
920: indeed, 920 is a multiple of itself, since 920 is evenly divisible by 920 (we have 920 / 920 = 1, so the remainder of this division is indeed zero)
1 840: indeed, 1 840 = 920 × 2
2 760: indeed, 2 760 = 920 × 3
3 680: indeed, 3 680 = 920 × 4
4 600: indeed, 4 600 = 920 × 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 920). 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 30.332). 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 920

Preceding numbers: …918, 919
Following numbers: 921, 922…

Nearest numbers from 920

Preceding prime number: 919
Following prime number: 929