Is 497 a prime number?

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

For 497, the answer is: No, 497 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 497) is as follows: 1, 7, 71, 497.

For 497 to be a prime number, it would have been required that 497 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

497 is a multiple of 1
497 is a multiple of 7
497 is a multiple of 71

For 497 to be a prime number, it would have been required that 497 has only two divisors, i.e., itself and 1.

However, 497 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 497 = 7 x 71, where 7 and 71 are both prime numbers.

Is 497 a deficient number?

Yes, 497 is a deficient number, that is to say 497 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 497 without 497 itself (that is 1 + 7 + 71 = 79).

Parity of 497

497 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 497 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 497 is about 22.293.

Thus, the square root of 497 is not an integer, and therefore 497 is not a square number.

What is the square number of 497?

The square of a number (here 497) is the result of the product of this number (497) by itself (i.e., 497 × 497); the square of 497 is sometimes called "raising 497 to the power 2", or "497 squared".

The square of 497 is 247 009 because 497 × 497 = 497² = 247 009.

As a consequence, 497 is the square root of 247 009.

Number of digits of 497

497 is a number with 3 digits.

What are the multiples of 497?

The multiples of 497 are all integers evenly divisible by 497, that is all numbers such that the remainder of the division by 497 is zero. There are infinitely many multiples of 497. The smallest multiples of 497 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 497 too, since 0 × 497 = 0
497: indeed, 497 is a multiple of itself, since 497 is evenly divisible by 497 (we have 497 / 497 = 1, so the remainder of this division is indeed zero)
994: indeed, 994 = 497 × 2
1 491: indeed, 1 491 = 497 × 3
1 988: indeed, 1 988 = 497 × 4
2 485: indeed, 2 485 = 497 × 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 497). 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 22.293). 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 497

Preceding numbers: …495, 496
Following numbers: 498, 499…

Nearest numbers from 497

Preceding prime number: 491
Following prime number: 499