Is 700 a prime number?

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

For 700, the answer is: No, 700 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 700) is as follows: 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700.

For 700 to be a prime number, it would have been required that 700 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 700 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 700 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

700 is a multiple of 1
700 is a multiple of 2
700 is a multiple of 4
700 is a multiple of 5
700 is a multiple of 7
700 is a multiple of 10
700 is a multiple of 14
700 is a multiple of 20
700 is a multiple of 25
700 is a multiple of 28
700 is a multiple of 35
700 is a multiple of 50
700 is a multiple of 70
700 is a multiple of 100
700 is a multiple of 140
700 is a multiple of 175
700 is a multiple of 350

For 700 to be a prime number, it would have been required that 700 has only two divisors, i.e., itself and 1.

Is 700 a deficient number?

No, 700 is not a deficient number: to be deficient, 700 should have been such that 700 is larger than the sum of its proper divisors, i.e., the divisors of 700 without 700 itself (that is 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 25 + 28 + 35 + 50 + 70 + 100 + 140 + 175 + 350 = 1 036).

In fact, 700 is an abundant number; 700 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 25 + 28 + 35 + 50 + 70 + 100 + 140 + 175 + 350 = 1 036). The smallest abundant number is 12.

Parity of 700

700 is an even number, because it is evenly divisible by 2: 700 / 2 = 350.

Find out more:

What is an even number?

Is 700 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 700 is about 26.458.

Thus, the square root of 700 is not an integer, and therefore 700 is not a square number.

What is the square number of 700?

The square of a number (here 700) is the result of the product of this number (700) by itself (i.e., 700 × 700); the square of 700 is sometimes called "raising 700 to the power 2", or "700 squared".

The square of 700 is 490 000 because 700 × 700 = 700² = 490 000.

As a consequence, 700 is the square root of 490 000.

Number of digits of 700

700 is a number with 3 digits.

What are the multiples of 700?

The multiples of 700 are all integers evenly divisible by 700, that is all numbers such that the remainder of the division by 700 is zero. There are infinitely many multiples of 700. The smallest multiples of 700 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 700 too, since 0 × 700 = 0
700: indeed, 700 is a multiple of itself, since 700 is evenly divisible by 700 (we have 700 / 700 = 1, so the remainder of this division is indeed zero)
1 400: indeed, 1 400 = 700 × 2
2 100: indeed, 2 100 = 700 × 3
2 800: indeed, 2 800 = 700 × 4
3 500: indeed, 3 500 = 700 × 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 700). 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 26.458). 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 700

Preceding numbers: …698, 699
Following numbers: 701, 702…

Nearest numbers from 700

Preceding prime number: 691
Following prime number: 701