Is 462 a prime number?

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

For 462, the answer is: No, 462 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 462) is as follows: 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462.

For 462 to be a prime number, it would have been required that 462 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

462 is a multiple of 1
462 is a multiple of 2
462 is a multiple of 3
462 is a multiple of 6
462 is a multiple of 7
462 is a multiple of 11
462 is a multiple of 14
462 is a multiple of 21
462 is a multiple of 22
462 is a multiple of 33
462 is a multiple of 42
462 is a multiple of 66
462 is a multiple of 77
462 is a multiple of 154
462 is a multiple of 231

For 462 to be a prime number, it would have been required that 462 has only two divisors, i.e., itself and 1.

Is 462 a deficient number?

No, 462 is not a deficient number: to be deficient, 462 should have been such that 462 is larger than the sum of its proper divisors, i.e., the divisors of 462 without 462 itself (that is 1 + 2 + 3 + 6 + 7 + 11 + 14 + 21 + 22 + 33 + 42 + 66 + 77 + 154 + 231 = 690).

In fact, 462 is an abundant number; 462 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 7 + 11 + 14 + 21 + 22 + 33 + 42 + 66 + 77 + 154 + 231 = 690). The smallest abundant number is 12.

Parity of 462

462 is an even number, because it is evenly divisible by 2: 462 / 2 = 231.

Find out more:

What is an even number?

Is 462 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 462 is about 21.494.

Thus, the square root of 462 is not an integer, and therefore 462 is not a square number.

What is the square number of 462?

The square of a number (here 462) is the result of the product of this number (462) by itself (i.e., 462 × 462); the square of 462 is sometimes called "raising 462 to the power 2", or "462 squared".

The square of 462 is 213 444 because 462 × 462 = 462² = 213 444.

As a consequence, 462 is the square root of 213 444.

Number of digits of 462

462 is a number with 3 digits.

What are the multiples of 462?

The multiples of 462 are all integers evenly divisible by 462, that is all numbers such that the remainder of the division by 462 is zero. There are infinitely many multiples of 462. The smallest multiples of 462 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 462 too, since 0 × 462 = 0
462: indeed, 462 is a multiple of itself, since 462 is evenly divisible by 462 (we have 462 / 462 = 1, so the remainder of this division is indeed zero)
924: indeed, 924 = 462 × 2
1 386: indeed, 1 386 = 462 × 3
1 848: indeed, 1 848 = 462 × 4
2 310: indeed, 2 310 = 462 × 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 462). 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 21.494). 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 462

Preceding numbers: …460, 461
Following numbers: 463, 464…

Nearest numbers from 462

Preceding prime number: 461
Following prime number: 463