Is 784 a prime number?

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

For 784, the answer is: No, 784 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 784) is as follows: 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784.

For 784 to be a prime number, it would have been required that 784 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

784 is a multiple of 1
784 is a multiple of 2
784 is a multiple of 4
784 is a multiple of 7
784 is a multiple of 8
784 is a multiple of 14
784 is a multiple of 16
784 is a multiple of 28
784 is a multiple of 49
784 is a multiple of 56
784 is a multiple of 98
784 is a multiple of 112
784 is a multiple of 196
784 is a multiple of 392

For 784 to be a prime number, it would have been required that 784 has only two divisors, i.e., itself and 1.

Is 784 a deficient number?

No, 784 is not a deficient number: to be deficient, 784 should have been such that 784 is larger than the sum of its proper divisors, i.e., the divisors of 784 without 784 itself (that is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 49 + 56 + 98 + 112 + 196 + 392 = 983).

In fact, 784 is an abundant number; 784 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 49 + 56 + 98 + 112 + 196 + 392 = 983). The smallest abundant number is 12.

Parity of 784

784 is an even number, because it is evenly divisible by 2: 784 / 2 = 392.

Find out more:

What is an even number?

Is 784 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 784 is 28.

Therefore, the square root of 784 is an integer, and as a consequence 784 is a perfect square.

As a consequence, 28 is the square root of 784.

What is the square number of 784?

The square of a number (here 784) is the result of the product of this number (784) by itself (i.e., 784 × 784); the square of 784 is sometimes called "raising 784 to the power 2", or "784 squared".

The square of 784 is 614 656 because 784 × 784 = 784² = 614 656.

As a consequence, 784 is the square root of 614 656.

Number of digits of 784

784 is a number with 3 digits.

What are the multiples of 784?

The multiples of 784 are all integers evenly divisible by 784, that is all numbers such that the remainder of the division by 784 is zero. There are infinitely many multiples of 784. The smallest multiples of 784 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 784 too, since 0 × 784 = 0
784: indeed, 784 is a multiple of itself, since 784 is evenly divisible by 784 (we have 784 / 784 = 1, so the remainder of this division is indeed zero)
1 568: indeed, 1 568 = 784 × 2
2 352: indeed, 2 352 = 784 × 3
3 136: indeed, 3 136 = 784 × 4
3 920: indeed, 3 920 = 784 × 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 784). 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 28). 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 784

Preceding numbers: …782, 783
Following numbers: 785, 786…

Nearest numbers from 784

Preceding prime number: 773
Following prime number: 787