Is 772 a prime number?

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

For 772, the answer is: No, 772 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 772) is as follows: 1, 2, 4, 193, 386, 772.

For 772 to be a prime number, it would have been required that 772 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

772 is a multiple of 1
772 is a multiple of 2
772 is a multiple of 4
772 is a multiple of 193
772 is a multiple of 386

For 772 to be a prime number, it would have been required that 772 has only two divisors, i.e., itself and 1.

Is 772 a deficient number?

Yes, 772 is a deficient number, that is to say 772 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 772 without 772 itself (that is 1 + 2 + 4 + 193 + 386 = 586).

Parity of 772

772 is an even number, because it is evenly divisible by 2: 772 / 2 = 386.

Find out more:

What is an even number?

Is 772 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 772 is about 27.785.

Thus, the square root of 772 is not an integer, and therefore 772 is not a square number.

What is the square number of 772?

The square of a number (here 772) is the result of the product of this number (772) by itself (i.e., 772 × 772); the square of 772 is sometimes called "raising 772 to the power 2", or "772 squared".

The square of 772 is 595 984 because 772 × 772 = 772² = 595 984.

As a consequence, 772 is the square root of 595 984.

Number of digits of 772

772 is a number with 3 digits.

What are the multiples of 772?

The multiples of 772 are all integers evenly divisible by 772, that is all numbers such that the remainder of the division by 772 is zero. There are infinitely many multiples of 772. The smallest multiples of 772 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 772 too, since 0 × 772 = 0
772: indeed, 772 is a multiple of itself, since 772 is evenly divisible by 772 (we have 772 / 772 = 1, so the remainder of this division is indeed zero)
1 544: indeed, 1 544 = 772 × 2
2 316: indeed, 2 316 = 772 × 3
3 088: indeed, 3 088 = 772 × 4
3 860: indeed, 3 860 = 772 × 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 772). 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 27.785). 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 772

Preceding numbers: …770, 771
Following numbers: 773, 774…

Nearest numbers from 772

Preceding prime number: 769
Following prime number: 773