Is 771 a prime number?

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

For 771, the answer is: No, 771 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 771) is as follows: 1, 3, 257, 771.

For 771 to be a prime number, it would have been required that 771 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

771 is a multiple of 1
771 is a multiple of 3
771 is a multiple of 257

For 771 to be a prime number, it would have been required that 771 has only two divisors, i.e., itself and 1.

However, 771 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 771 = 3 x 257, where 3 and 257 are both prime numbers.

Is 771 a deficient number?

Yes, 771 is a deficient number, that is to say 771 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 771 without 771 itself (that is 1 + 3 + 257 = 261).

Parity of 771

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

Find out more:

What is an even number?

Is 771 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 771 is about 27.767.

Thus, the square root of 771 is not an integer, and therefore 771 is not a square number.

What is the square number of 771?

The square of a number (here 771) is the result of the product of this number (771) by itself (i.e., 771 × 771); the square of 771 is sometimes called "raising 771 to the power 2", or "771 squared".

The square of 771 is 594 441 because 771 × 771 = 771² = 594 441.

As a consequence, 771 is the square root of 594 441.

Number of digits of 771

771 is a number with 3 digits.

What are the multiples of 771?

The multiples of 771 are all integers evenly divisible by 771, that is all numbers such that the remainder of the division by 771 is zero. There are infinitely many multiples of 771. The smallest multiples of 771 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 771 too, since 0 × 771 = 0
771: indeed, 771 is a multiple of itself, since 771 is evenly divisible by 771 (we have 771 / 771 = 1, so the remainder of this division is indeed zero)
1 542: indeed, 1 542 = 771 × 2
2 313: indeed, 2 313 = 771 × 3
3 084: indeed, 3 084 = 771 × 4
3 855: indeed, 3 855 = 771 × 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 771). 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 27.767). 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 771

Preceding numbers: …769, 770
Following numbers: 772, 773…

Nearest numbers from 771

Preceding prime number: 769
Following prime number: 773