Is 763 a prime number?

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

For 763, the answer is: No, 763 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 763) is as follows: 1, 7, 109, 763.

For 763 to be a prime number, it would have been required that 763 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

763 is a multiple of 1
763 is a multiple of 7
763 is a multiple of 109

For 763 to be a prime number, it would have been required that 763 has only two divisors, i.e., itself and 1.

However, 763 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 763 = 7 x 109, where 7 and 109 are both prime numbers.

Is 763 a deficient number?

Yes, 763 is a deficient number, that is to say 763 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 763 without 763 itself (that is 1 + 7 + 109 = 117).

Parity of 763

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

Find out more:

What is an even number?

Is 763 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 763 is about 27.622.

Thus, the square root of 763 is not an integer, and therefore 763 is not a square number.

What is the square number of 763?

The square of a number (here 763) is the result of the product of this number (763) by itself (i.e., 763 × 763); the square of 763 is sometimes called "raising 763 to the power 2", or "763 squared".

The square of 763 is 582 169 because 763 × 763 = 763² = 582 169.

As a consequence, 763 is the square root of 582 169.

Number of digits of 763

763 is a number with 3 digits.

What are the multiples of 763?

The multiples of 763 are all integers evenly divisible by 763, that is all numbers such that the remainder of the division by 763 is zero. There are infinitely many multiples of 763. The smallest multiples of 763 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 763 too, since 0 × 763 = 0
763: indeed, 763 is a multiple of itself, since 763 is evenly divisible by 763 (we have 763 / 763 = 1, so the remainder of this division is indeed zero)
1 526: indeed, 1 526 = 763 × 2
2 289: indeed, 2 289 = 763 × 3
3 052: indeed, 3 052 = 763 × 4
3 815: indeed, 3 815 = 763 × 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 763). 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 27.622). 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 763

Preceding numbers: …761, 762
Following numbers: 764, 765…

Nearest numbers from 763

Preceding prime number: 761
Following prime number: 769