Is 698 a prime number?

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

For 698, the answer is: No, 698 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 698) is as follows: 1, 2, 349, 698.

For 698 to be a prime number, it would have been required that 698 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

698 is a multiple of 1
698 is a multiple of 2
698 is a multiple of 349

For 698 to be a prime number, it would have been required that 698 has only two divisors, i.e., itself and 1.

However, 698 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 698 = 2 x 349, where 2 and 349 are both prime numbers.

Is 698 a deficient number?

Yes, 698 is a deficient number, that is to say 698 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 698 without 698 itself (that is 1 + 2 + 349 = 352).

Parity of 698

698 is an even number, because it is evenly divisible by 2: 698 / 2 = 349.

Find out more:

What is an even number?

Is 698 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 698 is about 26.420.

Thus, the square root of 698 is not an integer, and therefore 698 is not a square number.

What is the square number of 698?

The square of a number (here 698) is the result of the product of this number (698) by itself (i.e., 698 × 698); the square of 698 is sometimes called "raising 698 to the power 2", or "698 squared".

The square of 698 is 487 204 because 698 × 698 = 698² = 487 204.

As a consequence, 698 is the square root of 487 204.

Number of digits of 698

698 is a number with 3 digits.

What are the multiples of 698?

The multiples of 698 are all integers evenly divisible by 698, that is all numbers such that the remainder of the division by 698 is zero. There are infinitely many multiples of 698. The smallest multiples of 698 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 698 too, since 0 × 698 = 0
698: indeed, 698 is a multiple of itself, since 698 is evenly divisible by 698 (we have 698 / 698 = 1, so the remainder of this division is indeed zero)
1 396: indeed, 1 396 = 698 × 2
2 094: indeed, 2 094 = 698 × 3
2 792: indeed, 2 792 = 698 × 4
3 490: indeed, 3 490 = 698 × 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 698). 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 26.420). 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 698

Preceding numbers: …696, 697
Following numbers: 699, 700…

Nearest numbers from 698

Preceding prime number: 691
Following prime number: 701