Is 407 a prime number?

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

For 407, the answer is: No, 407 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 407) is as follows: 1, 11, 37, 407.

For 407 to be a prime number, it would have been required that 407 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

407 is a multiple of 1
407 is a multiple of 11
407 is a multiple of 37

For 407 to be a prime number, it would have been required that 407 has only two divisors, i.e., itself and 1.

However, 407 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 407 = 11 x 37, where 11 and 37 are both prime numbers.

Is 407 a deficient number?

Yes, 407 is a deficient number, that is to say 407 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 407 without 407 itself (that is 1 + 11 + 37 = 49).

Parity of 407

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

Find out more:

What is an even number?

Is 407 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 407 is about 20.174.

Thus, the square root of 407 is not an integer, and therefore 407 is not a square number.

What is the square number of 407?

The square of a number (here 407) is the result of the product of this number (407) by itself (i.e., 407 × 407); the square of 407 is sometimes called "raising 407 to the power 2", or "407 squared".

The square of 407 is 165 649 because 407 × 407 = 407² = 165 649.

As a consequence, 407 is the square root of 165 649.

Number of digits of 407

407 is a number with 3 digits.

What are the multiples of 407?

The multiples of 407 are all integers evenly divisible by 407, that is all numbers such that the remainder of the division by 407 is zero. There are infinitely many multiples of 407. The smallest multiples of 407 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 407 too, since 0 × 407 = 0
407: indeed, 407 is a multiple of itself, since 407 is evenly divisible by 407 (we have 407 / 407 = 1, so the remainder of this division is indeed zero)
814: indeed, 814 = 407 × 2
1 221: indeed, 1 221 = 407 × 3
1 628: indeed, 1 628 = 407 × 4
2 035: indeed, 2 035 = 407 × 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 407). 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 20.174). 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 407

Preceding numbers: …405, 406
Following numbers: 408, 409…

Nearest numbers from 407

Preceding prime number: 401
Following prime number: 409