Is 704 a prime number?

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

For 704, the answer is: No, 704 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 704) is as follows: 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704.

For 704 to be a prime number, it would have been required that 704 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

704 is a multiple of 1
704 is a multiple of 2
704 is a multiple of 4
704 is a multiple of 8
704 is a multiple of 11
704 is a multiple of 16
704 is a multiple of 22
704 is a multiple of 32
704 is a multiple of 44
704 is a multiple of 64
704 is a multiple of 88
704 is a multiple of 176
704 is a multiple of 352

For 704 to be a prime number, it would have been required that 704 has only two divisors, i.e., itself and 1.

Is 704 a deficient number?

No, 704 is not a deficient number: to be deficient, 704 should have been such that 704 is larger than the sum of its proper divisors, i.e., the divisors of 704 without 704 itself (that is 1 + 2 + 4 + 8 + 11 + 16 + 22 + 32 + 44 + 64 + 88 + 176 + 352 = 820).

In fact, 704 is an abundant number; 704 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 11 + 16 + 22 + 32 + 44 + 64 + 88 + 176 + 352 = 820). The smallest abundant number is 12.

Parity of 704

704 is an even number, because it is evenly divisible by 2: 704 / 2 = 352.

Find out more:

What is an even number?

Is 704 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 704 is about 26.533.

Thus, the square root of 704 is not an integer, and therefore 704 is not a square number.

What is the square number of 704?

The square of a number (here 704) is the result of the product of this number (704) by itself (i.e., 704 × 704); the square of 704 is sometimes called "raising 704 to the power 2", or "704 squared".

The square of 704 is 495 616 because 704 × 704 = 704² = 495 616.

As a consequence, 704 is the square root of 495 616.

Number of digits of 704

704 is a number with 3 digits.

What are the multiples of 704?

The multiples of 704 are all integers evenly divisible by 704, that is all numbers such that the remainder of the division by 704 is zero. There are infinitely many multiples of 704. The smallest multiples of 704 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 704 too, since 0 × 704 = 0
704: indeed, 704 is a multiple of itself, since 704 is evenly divisible by 704 (we have 704 / 704 = 1, so the remainder of this division is indeed zero)
1 408: indeed, 1 408 = 704 × 2
2 112: indeed, 2 112 = 704 × 3
2 816: indeed, 2 816 = 704 × 4
3 520: indeed, 3 520 = 704 × 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 704). 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 26.533). 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 704

Preceding numbers: …702, 703
Following numbers: 705, 706…

Nearest numbers from 704

Preceding prime number: 701
Following prime number: 709