Is 767 a prime number?

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

For 767, the answer is: No, 767 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 767) is as follows: 1, 13, 59, 767.

For 767 to be a prime number, it would have been required that 767 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

767 is a multiple of 1
767 is a multiple of 13
767 is a multiple of 59

For 767 to be a prime number, it would have been required that 767 has only two divisors, i.e., itself and 1.

However, 767 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 767 = 13 x 59, where 13 and 59 are both prime numbers.

Is 767 a deficient number?

Yes, 767 is a deficient number, that is to say 767 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 767 without 767 itself (that is 1 + 13 + 59 = 73).

Parity of 767

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

Find out more:

What is an even number?

Is 767 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 767 is about 27.695.

Thus, the square root of 767 is not an integer, and therefore 767 is not a square number.

What is the square number of 767?

The square of a number (here 767) is the result of the product of this number (767) by itself (i.e., 767 × 767); the square of 767 is sometimes called "raising 767 to the power 2", or "767 squared".

The square of 767 is 588 289 because 767 × 767 = 767² = 588 289.

As a consequence, 767 is the square root of 588 289.

Number of digits of 767

767 is a number with 3 digits.

What are the multiples of 767?

The multiples of 767 are all integers evenly divisible by 767, that is all numbers such that the remainder of the division by 767 is zero. There are infinitely many multiples of 767. The smallest multiples of 767 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 767 too, since 0 × 767 = 0
767: indeed, 767 is a multiple of itself, since 767 is evenly divisible by 767 (we have 767 / 767 = 1, so the remainder of this division is indeed zero)
1 534: indeed, 1 534 = 767 × 2
2 301: indeed, 2 301 = 767 × 3
3 068: indeed, 3 068 = 767 × 4
3 835: indeed, 3 835 = 767 × 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 767). 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 27.695). 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 767

Preceding numbers: …765, 766
Following numbers: 768, 769…

Nearest numbers from 767

Preceding prime number: 761
Following prime number: 769