Is 791 a prime number?

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

For 791, the answer is: No, 791 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 791) is as follows: 1, 7, 113, 791.

For 791 to be a prime number, it would have been required that 791 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

791 is a multiple of 1
791 is a multiple of 7
791 is a multiple of 113

For 791 to be a prime number, it would have been required that 791 has only two divisors, i.e., itself and 1.

However, 791 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 791 = 7 x 113, where 7 and 113 are both prime numbers.

Is 791 a deficient number?

Yes, 791 is a deficient number, that is to say 791 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 791 without 791 itself (that is 1 + 7 + 113 = 121).

Parity of 791

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

Find out more:

What is an even number?

Is 791 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 791 is about 28.125.

Thus, the square root of 791 is not an integer, and therefore 791 is not a square number.

What is the square number of 791?

The square of a number (here 791) is the result of the product of this number (791) by itself (i.e., 791 × 791); the square of 791 is sometimes called "raising 791 to the power 2", or "791 squared".

The square of 791 is 625 681 because 791 × 791 = 791² = 625 681.

As a consequence, 791 is the square root of 625 681.

Number of digits of 791

791 is a number with 3 digits.

What are the multiples of 791?

The multiples of 791 are all integers evenly divisible by 791, that is all numbers such that the remainder of the division by 791 is zero. There are infinitely many multiples of 791. The smallest multiples of 791 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 791 too, since 0 × 791 = 0
791: indeed, 791 is a multiple of itself, since 791 is evenly divisible by 791 (we have 791 / 791 = 1, so the remainder of this division is indeed zero)
1 582: indeed, 1 582 = 791 × 2
2 373: indeed, 2 373 = 791 × 3
3 164: indeed, 3 164 = 791 × 4
3 955: indeed, 3 955 = 791 × 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 791). 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 28.125). 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 791

Preceding numbers: …789, 790
Following numbers: 792, 793…

Nearest numbers from 791

Preceding prime number: 787
Following prime number: 797