Is 490 a prime number?

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

For 490, the answer is: No, 490 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 490) is as follows: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490.

For 490 to be a prime number, it would have been required that 490 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 490 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 490 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

490 is a multiple of 1
490 is a multiple of 2
490 is a multiple of 5
490 is a multiple of 7
490 is a multiple of 10
490 is a multiple of 14
490 is a multiple of 35
490 is a multiple of 49
490 is a multiple of 70
490 is a multiple of 98
490 is a multiple of 245

For 490 to be a prime number, it would have been required that 490 has only two divisors, i.e., itself and 1.

Is 490 a deficient number?

No, 490 is not a deficient number: to be deficient, 490 should have been such that 490 is larger than the sum of its proper divisors, i.e., the divisors of 490 without 490 itself (that is 1 + 2 + 5 + 7 + 10 + 14 + 35 + 49 + 70 + 98 + 245 = 536).

In fact, 490 is an abundant number; 490 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 5 + 7 + 10 + 14 + 35 + 49 + 70 + 98 + 245 = 536). The smallest abundant number is 12.

Parity of 490

490 is an even number, because it is evenly divisible by 2: 490 / 2 = 245.

Find out more:

What is an even number?

Is 490 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 490 is about 22.136.

Thus, the square root of 490 is not an integer, and therefore 490 is not a square number.

What is the square number of 490?

The square of a number (here 490) is the result of the product of this number (490) by itself (i.e., 490 × 490); the square of 490 is sometimes called "raising 490 to the power 2", or "490 squared".

The square of 490 is 240 100 because 490 × 490 = 490² = 240 100.

As a consequence, 490 is the square root of 240 100.

Number of digits of 490

490 is a number with 3 digits.

What are the multiples of 490?

The multiples of 490 are all integers evenly divisible by 490, that is all numbers such that the remainder of the division by 490 is zero. There are infinitely many multiples of 490. The smallest multiples of 490 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 490 too, since 0 × 490 = 0
490: indeed, 490 is a multiple of itself, since 490 is evenly divisible by 490 (we have 490 / 490 = 1, so the remainder of this division is indeed zero)
980: indeed, 980 = 490 × 2
1 470: indeed, 1 470 = 490 × 3
1 960: indeed, 1 960 = 490 × 4
2 450: indeed, 2 450 = 490 × 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 490). 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 22.136). 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 490

Preceding numbers: …488, 489
Following numbers: 491, 492…

Nearest numbers from 490

Preceding prime number: 487
Following prime number: 491