Is 352 a prime number?

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

For 352, the answer is: No, 352 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 352) is as follows: 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352.

For 352 to be a prime number, it would have been required that 352 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

352 is a multiple of 1
352 is a multiple of 2
352 is a multiple of 4
352 is a multiple of 8
352 is a multiple of 11
352 is a multiple of 16
352 is a multiple of 22
352 is a multiple of 32
352 is a multiple of 44
352 is a multiple of 88
352 is a multiple of 176

For 352 to be a prime number, it would have been required that 352 has only two divisors, i.e., itself and 1.

Is 352 a deficient number?

No, 352 is not a deficient number: to be deficient, 352 should have been such that 352 is larger than the sum of its proper divisors, i.e., the divisors of 352 without 352 itself (that is 1 + 2 + 4 + 8 + 11 + 16 + 22 + 32 + 44 + 88 + 176 = 404).

In fact, 352 is an abundant number; 352 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 11 + 16 + 22 + 32 + 44 + 88 + 176 = 404). The smallest abundant number is 12.

Parity of 352

352 is an even number, because it is evenly divisible by 2: 352 / 2 = 176.

Find out more:

What is an even number?

Is 352 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 352 is about 18.762.

Thus, the square root of 352 is not an integer, and therefore 352 is not a square number.

What is the square number of 352?

The square of a number (here 352) is the result of the product of this number (352) by itself (i.e., 352 × 352); the square of 352 is sometimes called "raising 352 to the power 2", or "352 squared".

The square of 352 is 123 904 because 352 × 352 = 352² = 123 904.

As a consequence, 352 is the square root of 123 904.

Number of digits of 352

352 is a number with 3 digits.

What are the multiples of 352?

The multiples of 352 are all integers evenly divisible by 352, that is all numbers such that the remainder of the division by 352 is zero. There are infinitely many multiples of 352. The smallest multiples of 352 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 352 too, since 0 × 352 = 0
352: indeed, 352 is a multiple of itself, since 352 is evenly divisible by 352 (we have 352 / 352 = 1, so the remainder of this division is indeed zero)
704: indeed, 704 = 352 × 2
1 056: indeed, 1 056 = 352 × 3
1 408: indeed, 1 408 = 352 × 4
1 760: indeed, 1 760 = 352 × 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 352). 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 18.762). 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 352

Preceding numbers: …350, 351
Following numbers: 353, 354…

Nearest numbers from 352

Preceding prime number: 349
Following prime number: 353