Is 648 a prime number?

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

For 648, the answer is: No, 648 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 648) is as follows: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648.

For 648 to be a prime number, it would have been required that 648 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

648 is a multiple of 1
648 is a multiple of 2
648 is a multiple of 3
648 is a multiple of 4
648 is a multiple of 6
648 is a multiple of 8
648 is a multiple of 9
648 is a multiple of 12
648 is a multiple of 18
648 is a multiple of 24
648 is a multiple of 27
648 is a multiple of 36
648 is a multiple of 54
648 is a multiple of 72
648 is a multiple of 81
648 is a multiple of 108
648 is a multiple of 162
648 is a multiple of 216
648 is a multiple of 324

For 648 to be a prime number, it would have been required that 648 has only two divisors, i.e., itself and 1.

Is 648 a deficient number?

No, 648 is not a deficient number: to be deficient, 648 should have been such that 648 is larger than the sum of its proper divisors, i.e., the divisors of 648 without 648 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 81 + 108 + 162 + 216 + 324 = 1 167).

In fact, 648 is an abundant number; 648 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 81 + 108 + 162 + 216 + 324 = 1 167). The smallest abundant number is 12.

Parity of 648

648 is an even number, because it is evenly divisible by 2: 648 / 2 = 324.

Find out more:

What is an even number?

Is 648 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 648 is about 25.456.

Thus, the square root of 648 is not an integer, and therefore 648 is not a square number.

What is the square number of 648?

The square of a number (here 648) is the result of the product of this number (648) by itself (i.e., 648 × 648); the square of 648 is sometimes called "raising 648 to the power 2", or "648 squared".

The square of 648 is 419 904 because 648 × 648 = 648² = 419 904.

As a consequence, 648 is the square root of 419 904.

Number of digits of 648

648 is a number with 3 digits.

What are the multiples of 648?

The multiples of 648 are all integers evenly divisible by 648, that is all numbers such that the remainder of the division by 648 is zero. There are infinitely many multiples of 648. The smallest multiples of 648 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 648 too, since 0 × 648 = 0
648: indeed, 648 is a multiple of itself, since 648 is evenly divisible by 648 (we have 648 / 648 = 1, so the remainder of this division is indeed zero)
1 296: indeed, 1 296 = 648 × 2
1 944: indeed, 1 944 = 648 × 3
2 592: indeed, 2 592 = 648 × 4
3 240: indeed, 3 240 = 648 × 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 648). 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 25.456). 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 648

Preceding numbers: …646, 647
Following numbers: 649, 650…

Nearest numbers from 648

Preceding prime number: 647
Following prime number: 653