Is 660 a prime number?

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

For 660, the answer is: No, 660 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 660) is as follows: 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660.

For 660 to be a prime number, it would have been required that 660 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 660 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 660 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

660 is a multiple of 1
660 is a multiple of 2
660 is a multiple of 3
660 is a multiple of 4
660 is a multiple of 5
660 is a multiple of 6
660 is a multiple of 10
660 is a multiple of 11
660 is a multiple of 12
660 is a multiple of 15
660 is a multiple of 20
660 is a multiple of 22
660 is a multiple of 30
660 is a multiple of 33
660 is a multiple of 44
660 is a multiple of 55
660 is a multiple of 60
660 is a multiple of 66
660 is a multiple of 110
660 is a multiple of 132
660 is a multiple of 165
660 is a multiple of 220
660 is a multiple of 330

For 660 to be a prime number, it would have been required that 660 has only two divisors, i.e., itself and 1.

Is 660 a deficient number?

No, 660 is not a deficient number: to be deficient, 660 should have been such that 660 is larger than the sum of its proper divisors, i.e., the divisors of 660 without 660 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 10 + 11 + 12 + 15 + 20 + 22 + 30 + 33 + 44 + 55 + 60 + 66 + 110 + 132 + 165 + 220 + 330 = 1 356).

In fact, 660 is an abundant number; 660 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 10 + 11 + 12 + 15 + 20 + 22 + 30 + 33 + 44 + 55 + 60 + 66 + 110 + 132 + 165 + 220 + 330 = 1 356). The smallest abundant number is 12.

Parity of 660

660 is an even number, because it is evenly divisible by 2: 660 / 2 = 330.

Find out more:

What is an even number?

Is 660 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 660 is about 25.690.

Thus, the square root of 660 is not an integer, and therefore 660 is not a square number.

What is the square number of 660?

The square of a number (here 660) is the result of the product of this number (660) by itself (i.e., 660 × 660); the square of 660 is sometimes called "raising 660 to the power 2", or "660 squared".

The square of 660 is 435 600 because 660 × 660 = 660² = 435 600.

As a consequence, 660 is the square root of 435 600.

Number of digits of 660

660 is a number with 3 digits.

What are the multiples of 660?

The multiples of 660 are all integers evenly divisible by 660, that is all numbers such that the remainder of the division by 660 is zero. There are infinitely many multiples of 660. The smallest multiples of 660 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 660 too, since 0 × 660 = 0
660: indeed, 660 is a multiple of itself, since 660 is evenly divisible by 660 (we have 660 / 660 = 1, so the remainder of this division is indeed zero)
1 320: indeed, 1 320 = 660 × 2
1 980: indeed, 1 980 = 660 × 3
2 640: indeed, 2 640 = 660 × 4
3 300: indeed, 3 300 = 660 × 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 660). 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 25.690). 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 660

Preceding numbers: …658, 659
Following numbers: 661, 662…

Nearest numbers from 660

Preceding prime number: 659
Following prime number: 661