Is 710 a prime number?

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

For 710, the answer is: No, 710 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 710) is as follows: 1, 2, 5, 10, 71, 142, 355, 710.

For 710 to be a prime number, it would have been required that 710 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 710 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 710 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

710 is a multiple of 1
710 is a multiple of 2
710 is a multiple of 5
710 is a multiple of 10
710 is a multiple of 71
710 is a multiple of 142
710 is a multiple of 355

For 710 to be a prime number, it would have been required that 710 has only two divisors, i.e., itself and 1.

Is 710 a deficient number?

Yes, 710 is a deficient number, that is to say 710 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 710 without 710 itself (that is 1 + 2 + 5 + 10 + 71 + 142 + 355 = 586).

Parity of 710

710 is an even number, because it is evenly divisible by 2: 710 / 2 = 355.

Find out more:

What is an even number?

Is 710 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 710 is about 26.646.

Thus, the square root of 710 is not an integer, and therefore 710 is not a square number.

What is the square number of 710?

The square of a number (here 710) is the result of the product of this number (710) by itself (i.e., 710 × 710); the square of 710 is sometimes called "raising 710 to the power 2", or "710 squared".

The square of 710 is 504 100 because 710 × 710 = 710² = 504 100.

As a consequence, 710 is the square root of 504 100.

Number of digits of 710

710 is a number with 3 digits.

What are the multiples of 710?

The multiples of 710 are all integers evenly divisible by 710, that is all numbers such that the remainder of the division by 710 is zero. There are infinitely many multiples of 710. The smallest multiples of 710 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 710 too, since 0 × 710 = 0
710: indeed, 710 is a multiple of itself, since 710 is evenly divisible by 710 (we have 710 / 710 = 1, so the remainder of this division is indeed zero)
1 420: indeed, 1 420 = 710 × 2
2 130: indeed, 2 130 = 710 × 3
2 840: indeed, 2 840 = 710 × 4
3 550: indeed, 3 550 = 710 × 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 710). 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 26.646). 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 710

Preceding numbers: …708, 709
Following numbers: 711, 712…

Nearest numbers from 710

Preceding prime number: 709
Following prime number: 719