Is 781 a prime number?

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

For 781, the answer is: No, 781 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 781) is as follows: 1, 11, 71, 781.

For 781 to be a prime number, it would have been required that 781 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

781 is a multiple of 1
781 is a multiple of 11
781 is a multiple of 71

For 781 to be a prime number, it would have been required that 781 has only two divisors, i.e., itself and 1.

However, 781 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 781 = 11 x 71, where 11 and 71 are both prime numbers.

Is 781 a deficient number?

Yes, 781 is a deficient number, that is to say 781 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 781 without 781 itself (that is 1 + 11 + 71 = 83).

Parity of 781

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

Find out more:

What is an even number?

Is 781 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 781 is about 27.946.

Thus, the square root of 781 is not an integer, and therefore 781 is not a square number.

What is the square number of 781?

The square of a number (here 781) is the result of the product of this number (781) by itself (i.e., 781 × 781); the square of 781 is sometimes called "raising 781 to the power 2", or "781 squared".

The square of 781 is 609 961 because 781 × 781 = 781² = 609 961.

As a consequence, 781 is the square root of 609 961.

Number of digits of 781

781 is a number with 3 digits.

What are the multiples of 781?

The multiples of 781 are all integers evenly divisible by 781, that is all numbers such that the remainder of the division by 781 is zero. There are infinitely many multiples of 781. The smallest multiples of 781 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 781 too, since 0 × 781 = 0
781: indeed, 781 is a multiple of itself, since 781 is evenly divisible by 781 (we have 781 / 781 = 1, so the remainder of this division is indeed zero)
1 562: indeed, 1 562 = 781 × 2
2 343: indeed, 2 343 = 781 × 3
3 124: indeed, 3 124 = 781 × 4
3 905: indeed, 3 905 = 781 × 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 781). 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 27.946). 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 781

Preceding numbers: …779, 780
Following numbers: 782, 783…

Nearest numbers from 781

Preceding prime number: 773
Following prime number: 787