Is 488 a prime number?

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

For 488, the answer is: No, 488 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 488) is as follows: 1, 2, 4, 8, 61, 122, 244, 488.

For 488 to be a prime number, it would have been required that 488 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

488 is a multiple of 1
488 is a multiple of 2
488 is a multiple of 4
488 is a multiple of 8
488 is a multiple of 61
488 is a multiple of 122
488 is a multiple of 244

For 488 to be a prime number, it would have been required that 488 has only two divisors, i.e., itself and 1.

Is 488 a deficient number?

Yes, 488 is a deficient number, that is to say 488 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 488 without 488 itself (that is 1 + 2 + 4 + 8 + 61 + 122 + 244 = 442).

Parity of 488

488 is an even number, because it is evenly divisible by 2: 488 / 2 = 244.

Find out more:

What is an even number?

Is 488 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 488 is about 22.091.

Thus, the square root of 488 is not an integer, and therefore 488 is not a square number.

What is the square number of 488?

The square of a number (here 488) is the result of the product of this number (488) by itself (i.e., 488 × 488); the square of 488 is sometimes called "raising 488 to the power 2", or "488 squared".

The square of 488 is 238 144 because 488 × 488 = 488² = 238 144.

As a consequence, 488 is the square root of 238 144.

Number of digits of 488

488 is a number with 3 digits.

What are the multiples of 488?

The multiples of 488 are all integers evenly divisible by 488, that is all numbers such that the remainder of the division by 488 is zero. There are infinitely many multiples of 488. The smallest multiples of 488 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 488 too, since 0 × 488 = 0
488: indeed, 488 is a multiple of itself, since 488 is evenly divisible by 488 (we have 488 / 488 = 1, so the remainder of this division is indeed zero)
976: indeed, 976 = 488 × 2
1 464: indeed, 1 464 = 488 × 3
1 952: indeed, 1 952 = 488 × 4
2 440: indeed, 2 440 = 488 × 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 488). 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 22.091). 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 488

Preceding numbers: …486, 487
Following numbers: 489, 490…

Nearest numbers from 488

Preceding prime number: 487
Following prime number: 491