Is 720 a prime number?

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

For 720, the answer is: No, 720 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 720) is as follows: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720.

For 720 to be a prime number, it would have been required that 720 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 720 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 720 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

720 is a multiple of 1
720 is a multiple of 2
720 is a multiple of 3
720 is a multiple of 4
720 is a multiple of 5
720 is a multiple of 6
720 is a multiple of 8
720 is a multiple of 9
720 is a multiple of 10
720 is a multiple of 12
720 is a multiple of 15
720 is a multiple of 16
720 is a multiple of 18
720 is a multiple of 20
720 is a multiple of 24
720 is a multiple of 30
720 is a multiple of 36
720 is a multiple of 40
720 is a multiple of 45
720 is a multiple of 48
720 is a multiple of 60
720 is a multiple of 72
720 is a multiple of 80
720 is a multiple of 90
720 is a multiple of 120
720 is a multiple of 144
720 is a multiple of 180
720 is a multiple of 240
720 is a multiple of 360

For 720 to be a prime number, it would have been required that 720 has only two divisors, i.e., itself and 1.

Is 720 a deficient number?

No, 720 is not a deficient number: to be deficient, 720 should have been such that 720 is larger than the sum of its proper divisors, i.e., the divisors of 720 without 720 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 48 + 60 + 72 + 80 + 90 + 120 + 144 + 180 + 240 + 360 = 1 698).

In fact, 720 is an abundant number; 720 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 48 + 60 + 72 + 80 + 90 + 120 + 144 + 180 + 240 + 360 = 1 698). The smallest abundant number is 12.

Parity of 720

720 is an even number, because it is evenly divisible by 2: 720 / 2 = 360.

Find out more:

What is an even number?

Is 720 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 720 is about 26.833.

Thus, the square root of 720 is not an integer, and therefore 720 is not a square number.

What is the square number of 720?

The square of a number (here 720) is the result of the product of this number (720) by itself (i.e., 720 × 720); the square of 720 is sometimes called "raising 720 to the power 2", or "720 squared".

The square of 720 is 518 400 because 720 × 720 = 720² = 518 400.

As a consequence, 720 is the square root of 518 400.

Number of digits of 720

720 is a number with 3 digits.

What are the multiples of 720?

The multiples of 720 are all integers evenly divisible by 720, that is all numbers such that the remainder of the division by 720 is zero. There are infinitely many multiples of 720. The smallest multiples of 720 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 720 too, since 0 × 720 = 0
720: indeed, 720 is a multiple of itself, since 720 is evenly divisible by 720 (we have 720 / 720 = 1, so the remainder of this division is indeed zero)
1 440: indeed, 1 440 = 720 × 2
2 160: indeed, 2 160 = 720 × 3
2 880: indeed, 2 880 = 720 × 4
3 600: indeed, 3 600 = 720 × 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 720). 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 26.833). 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 720

Preceding numbers: …718, 719
Following numbers: 721, 722…

Nearest numbers from 720

Preceding prime number: 719
Following prime number: 727