Is 496 a prime number?

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

For 496, the answer is: No, 496 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 496) is as follows: 1, 2, 4, 8, 16, 31, 62, 124, 248, 496.

For 496 to be a prime number, it would have been required that 496 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

496 is a multiple of 1
496 is a multiple of 2
496 is a multiple of 4
496 is a multiple of 8
496 is a multiple of 16
496 is a multiple of 31
496 is a multiple of 62
496 is a multiple of 124
496 is a multiple of 248

For 496 to be a prime number, it would have been required that 496 has only two divisors, i.e., itself and 1.

Is 496 a deficient number?

No, 496 is not a deficient number: to be deficient, 496 should have been such that 496 is larger than the sum of its proper divisors, i.e., the divisors of 496 without 496 itself (that is 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496).

Is 496 a perfect number?

Yes, 496 is a perfect number, that is to day 496 equals the sum of its proper positive divisors, i.e., the sum of its divisors excluding 496 itself.

Indeed, 496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248.

Note that perfect numbers are very rare: there are only 4 perfect numbers smaller than 1 000 000, viz., 6, 28, 496 and 8 128. Then, the next perfect number is already 33 550 336!

Parity of 496

496 is an even number, because it is evenly divisible by 2: 496 / 2 = 248.

Find out more:

What is an even number?

Is 496 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 496 is about 22.271.

Thus, the square root of 496 is not an integer, and therefore 496 is not a square number.

What is the square number of 496?

The square of a number (here 496) is the result of the product of this number (496) by itself (i.e., 496 × 496); the square of 496 is sometimes called "raising 496 to the power 2", or "496 squared".

The square of 496 is 246 016 because 496 × 496 = 496² = 246 016.

As a consequence, 496 is the square root of 246 016.

Number of digits of 496

496 is a number with 3 digits.

What are the multiples of 496?

The multiples of 496 are all integers evenly divisible by 496, that is all numbers such that the remainder of the division by 496 is zero. There are infinitely many multiples of 496. The smallest multiples of 496 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 496 too, since 0 × 496 = 0
496: indeed, 496 is a multiple of itself, since 496 is evenly divisible by 496 (we have 496 / 496 = 1, so the remainder of this division is indeed zero)
992: indeed, 992 = 496 × 2
1 488: indeed, 1 488 = 496 × 3
1 984: indeed, 1 984 = 496 × 4
2 480: indeed, 2 480 = 496 × 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 496). 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 22.271). 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 496

Preceding numbers: …494, 495
Following numbers: 497, 498…

Nearest numbers from 496

Preceding prime number: 491
Following prime number: 499