Is 493 a prime number?

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

For 493, the answer is: No, 493 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 493) is as follows: 1, 17, 29, 493.

For 493 to be a prime number, it would have been required that 493 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

493 is a multiple of 1
493 is a multiple of 17
493 is a multiple of 29

For 493 to be a prime number, it would have been required that 493 has only two divisors, i.e., itself and 1.

However, 493 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 493 = 17 x 29, where 17 and 29 are both prime numbers.

Is 493 a deficient number?

Yes, 493 is a deficient number, that is to say 493 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 493 without 493 itself (that is 1 + 17 + 29 = 47).

Parity of 493

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

Find out more:

What is an even number?

Is 493 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 493 is about 22.204.

Thus, the square root of 493 is not an integer, and therefore 493 is not a square number.

What is the square number of 493?

The square of a number (here 493) is the result of the product of this number (493) by itself (i.e., 493 × 493); the square of 493 is sometimes called "raising 493 to the power 2", or "493 squared".

The square of 493 is 243 049 because 493 × 493 = 493² = 243 049.

As a consequence, 493 is the square root of 243 049.

Number of digits of 493

493 is a number with 3 digits.

What are the multiples of 493?

The multiples of 493 are all integers evenly divisible by 493, that is all numbers such that the remainder of the division by 493 is zero. There are infinitely many multiples of 493. The smallest multiples of 493 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 493 too, since 0 × 493 = 0
493: indeed, 493 is a multiple of itself, since 493 is evenly divisible by 493 (we have 493 / 493 = 1, so the remainder of this division is indeed zero)
986: indeed, 986 = 493 × 2
1 479: indeed, 1 479 = 493 × 3
1 972: indeed, 1 972 = 493 × 4
2 465: indeed, 2 465 = 493 × 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 493). 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 22.204). 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 493

Preceding numbers: …491, 492
Following numbers: 494, 495…

Nearest numbers from 493

Preceding prime number: 491
Following prime number: 499