Is 782 a prime number?

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

For 782, the answer is: No, 782 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 782) is as follows: 1, 2, 17, 23, 34, 46, 391, 782.

For 782 to be a prime number, it would have been required that 782 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

782 is a multiple of 1
782 is a multiple of 2
782 is a multiple of 17
782 is a multiple of 23
782 is a multiple of 34
782 is a multiple of 46
782 is a multiple of 391

For 782 to be a prime number, it would have been required that 782 has only two divisors, i.e., itself and 1.

Is 782 a deficient number?

Yes, 782 is a deficient number, that is to say 782 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 782 without 782 itself (that is 1 + 2 + 17 + 23 + 34 + 46 + 391 = 514).

Parity of 782

782 is an even number, because it is evenly divisible by 2: 782 / 2 = 391.

Find out more:

What is an even number?

Is 782 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 782 is about 27.964.

Thus, the square root of 782 is not an integer, and therefore 782 is not a square number.

What is the square number of 782?

The square of a number (here 782) is the result of the product of this number (782) by itself (i.e., 782 × 782); the square of 782 is sometimes called "raising 782 to the power 2", or "782 squared".

The square of 782 is 611 524 because 782 × 782 = 782² = 611 524.

As a consequence, 782 is the square root of 611 524.

Number of digits of 782

782 is a number with 3 digits.

What are the multiples of 782?

The multiples of 782 are all integers evenly divisible by 782, that is all numbers such that the remainder of the division by 782 is zero. There are infinitely many multiples of 782. The smallest multiples of 782 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 782 too, since 0 × 782 = 0
782: indeed, 782 is a multiple of itself, since 782 is evenly divisible by 782 (we have 782 / 782 = 1, so the remainder of this division is indeed zero)
1 564: indeed, 1 564 = 782 × 2
2 346: indeed, 2 346 = 782 × 3
3 128: indeed, 3 128 = 782 × 4
3 910: indeed, 3 910 = 782 × 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 782). 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 27.964). 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 782

Preceding numbers: …780, 781
Following numbers: 783, 784…

Nearest numbers from 782

Preceding prime number: 773
Following prime number: 787