Is 702 a prime number?

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

For 702, the answer is: No, 702 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 702) is as follows: 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702.

For 702 to be a prime number, it would have been required that 702 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

702 is a multiple of 1
702 is a multiple of 2
702 is a multiple of 3
702 is a multiple of 6
702 is a multiple of 9
702 is a multiple of 13
702 is a multiple of 18
702 is a multiple of 26
702 is a multiple of 27
702 is a multiple of 39
702 is a multiple of 54
702 is a multiple of 78
702 is a multiple of 117
702 is a multiple of 234
702 is a multiple of 351

For 702 to be a prime number, it would have been required that 702 has only two divisors, i.e., itself and 1.

Is 702 a deficient number?

No, 702 is not a deficient number: to be deficient, 702 should have been such that 702 is larger than the sum of its proper divisors, i.e., the divisors of 702 without 702 itself (that is 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 27 + 39 + 54 + 78 + 117 + 234 + 351 = 978).

In fact, 702 is an abundant number; 702 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 27 + 39 + 54 + 78 + 117 + 234 + 351 = 978). The smallest abundant number is 12.

Parity of 702

702 is an even number, because it is evenly divisible by 2: 702 / 2 = 351.

Find out more:

What is an even number?

Is 702 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 702 is about 26.495.

Thus, the square root of 702 is not an integer, and therefore 702 is not a square number.

What is the square number of 702?

The square of a number (here 702) is the result of the product of this number (702) by itself (i.e., 702 × 702); the square of 702 is sometimes called "raising 702 to the power 2", or "702 squared".

The square of 702 is 492 804 because 702 × 702 = 702² = 492 804.

As a consequence, 702 is the square root of 492 804.

Number of digits of 702

702 is a number with 3 digits.

What are the multiples of 702?

The multiples of 702 are all integers evenly divisible by 702, that is all numbers such that the remainder of the division by 702 is zero. There are infinitely many multiples of 702. The smallest multiples of 702 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 702 too, since 0 × 702 = 0
702: indeed, 702 is a multiple of itself, since 702 is evenly divisible by 702 (we have 702 / 702 = 1, so the remainder of this division is indeed zero)
1 404: indeed, 1 404 = 702 × 2
2 106: indeed, 2 106 = 702 × 3
2 808: indeed, 2 808 = 702 × 4
3 510: indeed, 3 510 = 702 × 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 702). 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 26.495). 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 702

Preceding numbers: …700, 701
Following numbers: 703, 704…

Nearest numbers from 702

Preceding prime number: 701
Following prime number: 709