Is 789 a prime number?

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

For 789, the answer is: No, 789 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 789) is as follows: 1, 3, 263, 789.

For 789 to be a prime number, it would have been required that 789 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

789 is a multiple of 1
789 is a multiple of 3
789 is a multiple of 263

For 789 to be a prime number, it would have been required that 789 has only two divisors, i.e., itself and 1.

However, 789 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 789 = 3 x 263, where 3 and 263 are both prime numbers.

Is 789 a deficient number?

Yes, 789 is a deficient number, that is to say 789 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 789 without 789 itself (that is 1 + 3 + 263 = 267).

Parity of 789

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

Find out more:

What is an even number?

Is 789 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 789 is about 28.089.

Thus, the square root of 789 is not an integer, and therefore 789 is not a square number.

What is the square number of 789?

The square of a number (here 789) is the result of the product of this number (789) by itself (i.e., 789 × 789); the square of 789 is sometimes called "raising 789 to the power 2", or "789 squared".

The square of 789 is 622 521 because 789 × 789 = 789² = 622 521.

As a consequence, 789 is the square root of 622 521.

Number of digits of 789

789 is a number with 3 digits.

What are the multiples of 789?

The multiples of 789 are all integers evenly divisible by 789, that is all numbers such that the remainder of the division by 789 is zero. There are infinitely many multiples of 789. The smallest multiples of 789 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 789 too, since 0 × 789 = 0
789: indeed, 789 is a multiple of itself, since 789 is evenly divisible by 789 (we have 789 / 789 = 1, so the remainder of this division is indeed zero)
1 578: indeed, 1 578 = 789 × 2
2 367: indeed, 2 367 = 789 × 3
3 156: indeed, 3 156 = 789 × 4
3 945: indeed, 3 945 = 789 × 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 789). 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 28.089). 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 789

Preceding numbers: …787, 788
Following numbers: 790, 791…

Nearest numbers from 789

Preceding prime number: 787
Following prime number: 797