Is 768 a prime number?

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

For 768, the answer is: No, 768 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 768) is as follows: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768.

For 768 to be a prime number, it would have been required that 768 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

768 is a multiple of 1
768 is a multiple of 2
768 is a multiple of 3
768 is a multiple of 4
768 is a multiple of 6
768 is a multiple of 8
768 is a multiple of 12
768 is a multiple of 16
768 is a multiple of 24
768 is a multiple of 32
768 is a multiple of 48
768 is a multiple of 64
768 is a multiple of 96
768 is a multiple of 128
768 is a multiple of 192
768 is a multiple of 256
768 is a multiple of 384

For 768 to be a prime number, it would have been required that 768 has only two divisors, i.e., itself and 1.

Is 768 a deficient number?

No, 768 is not a deficient number: to be deficient, 768 should have been such that 768 is larger than the sum of its proper divisors, i.e., the divisors of 768 without 768 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 + 128 + 192 + 256 + 384 = 1 276).

In fact, 768 is an abundant number; 768 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 + 128 + 192 + 256 + 384 = 1 276). The smallest abundant number is 12.

Parity of 768

768 is an even number, because it is evenly divisible by 2: 768 / 2 = 384.

Find out more:

What is an even number?

Is 768 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 768 is about 27.713.

Thus, the square root of 768 is not an integer, and therefore 768 is not a square number.

What is the square number of 768?

The square of a number (here 768) is the result of the product of this number (768) by itself (i.e., 768 × 768); the square of 768 is sometimes called "raising 768 to the power 2", or "768 squared".

The square of 768 is 589 824 because 768 × 768 = 768² = 589 824.

As a consequence, 768 is the square root of 589 824.

Number of digits of 768

768 is a number with 3 digits.

What are the multiples of 768?

The multiples of 768 are all integers evenly divisible by 768, that is all numbers such that the remainder of the division by 768 is zero. There are infinitely many multiples of 768. The smallest multiples of 768 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 768 too, since 0 × 768 = 0
768: indeed, 768 is a multiple of itself, since 768 is evenly divisible by 768 (we have 768 / 768 = 1, so the remainder of this division is indeed zero)
1 536: indeed, 1 536 = 768 × 2
2 304: indeed, 2 304 = 768 × 3
3 072: indeed, 3 072 = 768 × 4
3 840: indeed, 3 840 = 768 × 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 768). 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 27.713). 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 768

Preceding numbers: …766, 767
Following numbers: 769, 770…

Nearest numbers from 768

Preceding prime number: 761
Following prime number: 769