Is 364 a prime number?

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

For 364, the answer is: No, 364 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 364) is as follows: 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364.

For 364 to be a prime number, it would have been required that 364 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

364 is a multiple of 1
364 is a multiple of 2
364 is a multiple of 4
364 is a multiple of 7
364 is a multiple of 13
364 is a multiple of 14
364 is a multiple of 26
364 is a multiple of 28
364 is a multiple of 52
364 is a multiple of 91
364 is a multiple of 182

For 364 to be a prime number, it would have been required that 364 has only two divisors, i.e., itself and 1.

Is 364 a deficient number?

No, 364 is not a deficient number: to be deficient, 364 should have been such that 364 is larger than the sum of its proper divisors, i.e., the divisors of 364 without 364 itself (that is 1 + 2 + 4 + 7 + 13 + 14 + 26 + 28 + 52 + 91 + 182 = 420).

In fact, 364 is an abundant number; 364 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 7 + 13 + 14 + 26 + 28 + 52 + 91 + 182 = 420). The smallest abundant number is 12.

Parity of 364

364 is an even number, because it is evenly divisible by 2: 364 / 2 = 182.

Find out more:

What is an even number?

Is 364 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 364 is about 19.079.

Thus, the square root of 364 is not an integer, and therefore 364 is not a square number.

What is the square number of 364?

The square of a number (here 364) is the result of the product of this number (364) by itself (i.e., 364 × 364); the square of 364 is sometimes called "raising 364 to the power 2", or "364 squared".

The square of 364 is 132 496 because 364 × 364 = 364² = 132 496.

As a consequence, 364 is the square root of 132 496.

Number of digits of 364

364 is a number with 3 digits.

What are the multiples of 364?

The multiples of 364 are all integers evenly divisible by 364, that is all numbers such that the remainder of the division by 364 is zero. There are infinitely many multiples of 364. The smallest multiples of 364 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 364 too, since 0 × 364 = 0
364: indeed, 364 is a multiple of itself, since 364 is evenly divisible by 364 (we have 364 / 364 = 1, so the remainder of this division is indeed zero)
728: indeed, 728 = 364 × 2
1 092: indeed, 1 092 = 364 × 3
1 456: indeed, 1 456 = 364 × 4
1 820: indeed, 1 820 = 364 × 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 364). 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 19.079). 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 364

Preceding numbers: …362, 363
Following numbers: 365, 366…

Nearest numbers from 364

Preceding prime number: 359
Following prime number: 367