Is 777 a prime number?

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

For 777, the answer is: No, 777 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 777) is as follows: 1, 3, 7, 21, 37, 111, 259, 777.

For 777 to be a prime number, it would have been required that 777 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

777 is a multiple of 1
777 is a multiple of 3
777 is a multiple of 7
777 is a multiple of 21
777 is a multiple of 37
777 is a multiple of 111
777 is a multiple of 259

For 777 to be a prime number, it would have been required that 777 has only two divisors, i.e., itself and 1.

Is 777 a deficient number?

Yes, 777 is a deficient number, that is to say 777 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 777 without 777 itself (that is 1 + 3 + 7 + 21 + 37 + 111 + 259 = 439).

Parity of 777

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

Find out more:

What is an even number?

Is 777 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 777 is about 27.875.

Thus, the square root of 777 is not an integer, and therefore 777 is not a square number.

What is the square number of 777?

The square of a number (here 777) is the result of the product of this number (777) by itself (i.e., 777 × 777); the square of 777 is sometimes called "raising 777 to the power 2", or "777 squared".

The square of 777 is 603 729 because 777 × 777 = 777² = 603 729.

As a consequence, 777 is the square root of 603 729.

Number of digits of 777

777 is a number with 3 digits.

What are the multiples of 777?

The multiples of 777 are all integers evenly divisible by 777, that is all numbers such that the remainder of the division by 777 is zero. There are infinitely many multiples of 777. The smallest multiples of 777 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 777 too, since 0 × 777 = 0
777: indeed, 777 is a multiple of itself, since 777 is evenly divisible by 777 (we have 777 / 777 = 1, so the remainder of this division is indeed zero)
1 554: indeed, 1 554 = 777 × 2
2 331: indeed, 2 331 = 777 × 3
3 108: indeed, 3 108 = 777 × 4
3 885: indeed, 3 885 = 777 × 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 777). 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 27.875). 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 777

Preceding numbers: …775, 776
Following numbers: 778, 779…

Nearest numbers from 777

Preceding prime number: 773
Following prime number: 787