Is 766 a prime number?

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

For 766, the answer is: No, 766 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 766) is as follows: 1, 2, 383, 766.

For 766 to be a prime number, it would have been required that 766 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

766 is a multiple of 1
766 is a multiple of 2
766 is a multiple of 383

For 766 to be a prime number, it would have been required that 766 has only two divisors, i.e., itself and 1.

However, 766 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 766 = 2 x 383, where 2 and 383 are both prime numbers.

Is 766 a deficient number?

Yes, 766 is a deficient number, that is to say 766 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 766 without 766 itself (that is 1 + 2 + 383 = 386).

Parity of 766

766 is an even number, because it is evenly divisible by 2: 766 / 2 = 383.

Find out more:

What is an even number?

Is 766 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 766 is about 27.677.

Thus, the square root of 766 is not an integer, and therefore 766 is not a square number.

What is the square number of 766?

The square of a number (here 766) is the result of the product of this number (766) by itself (i.e., 766 × 766); the square of 766 is sometimes called "raising 766 to the power 2", or "766 squared".

The square of 766 is 586 756 because 766 × 766 = 766² = 586 756.

As a consequence, 766 is the square root of 586 756.

Number of digits of 766

766 is a number with 3 digits.

What are the multiples of 766?

The multiples of 766 are all integers evenly divisible by 766, that is all numbers such that the remainder of the division by 766 is zero. There are infinitely many multiples of 766. The smallest multiples of 766 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 766 too, since 0 × 766 = 0
766: indeed, 766 is a multiple of itself, since 766 is evenly divisible by 766 (we have 766 / 766 = 1, so the remainder of this division is indeed zero)
1 532: indeed, 1 532 = 766 × 2
2 298: indeed, 2 298 = 766 × 3
3 064: indeed, 3 064 = 766 × 4
3 830: indeed, 3 830 = 766 × 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 766). 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 27.677). 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 766

Preceding numbers: …764, 765
Following numbers: 767, 768…

Nearest numbers from 766

Preceding prime number: 761
Following prime number: 769