Is 714 a prime number?

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

For 714, the answer is: No, 714 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 714) is as follows: 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714.

For 714 to be a prime number, it would have been required that 714 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

714 is a multiple of 1
714 is a multiple of 2
714 is a multiple of 3
714 is a multiple of 6
714 is a multiple of 7
714 is a multiple of 14
714 is a multiple of 17
714 is a multiple of 21
714 is a multiple of 34
714 is a multiple of 42
714 is a multiple of 51
714 is a multiple of 102
714 is a multiple of 119
714 is a multiple of 238
714 is a multiple of 357

For 714 to be a prime number, it would have been required that 714 has only two divisors, i.e., itself and 1.

Is 714 a deficient number?

No, 714 is not a deficient number: to be deficient, 714 should have been such that 714 is larger than the sum of its proper divisors, i.e., the divisors of 714 without 714 itself (that is 1 + 2 + 3 + 6 + 7 + 14 + 17 + 21 + 34 + 42 + 51 + 102 + 119 + 238 + 357 = 1 014).

In fact, 714 is an abundant number; 714 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 7 + 14 + 17 + 21 + 34 + 42 + 51 + 102 + 119 + 238 + 357 = 1 014). The smallest abundant number is 12.

Parity of 714

714 is an even number, because it is evenly divisible by 2: 714 / 2 = 357.

Find out more:

What is an even number?

Is 714 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 714 is about 26.721.

Thus, the square root of 714 is not an integer, and therefore 714 is not a square number.

What is the square number of 714?

The square of a number (here 714) is the result of the product of this number (714) by itself (i.e., 714 × 714); the square of 714 is sometimes called "raising 714 to the power 2", or "714 squared".

The square of 714 is 509 796 because 714 × 714 = 714² = 509 796.

As a consequence, 714 is the square root of 509 796.

Number of digits of 714

714 is a number with 3 digits.

What are the multiples of 714?

The multiples of 714 are all integers evenly divisible by 714, that is all numbers such that the remainder of the division by 714 is zero. There are infinitely many multiples of 714. The smallest multiples of 714 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 714 too, since 0 × 714 = 0
714: indeed, 714 is a multiple of itself, since 714 is evenly divisible by 714 (we have 714 / 714 = 1, so the remainder of this division is indeed zero)
1 428: indeed, 1 428 = 714 × 2
2 142: indeed, 2 142 = 714 × 3
2 856: indeed, 2 856 = 714 × 4
3 570: indeed, 3 570 = 714 × 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 714). 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 26.721). 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 714

Preceding numbers: …712, 713
Following numbers: 715, 716…

Nearest numbers from 714

Preceding prime number: 709
Following prime number: 719