Is 351 a prime number?

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

For 351, the answer is: No, 351 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 351) is as follows: 1, 3, 9, 13, 27, 39, 117, 351.

For 351 to be a prime number, it would have been required that 351 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

351 is a multiple of 1
351 is a multiple of 3
351 is a multiple of 9
351 is a multiple of 13
351 is a multiple of 27
351 is a multiple of 39
351 is a multiple of 117

For 351 to be a prime number, it would have been required that 351 has only two divisors, i.e., itself and 1.

Is 351 a deficient number?

Yes, 351 is a deficient number, that is to say 351 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 351 without 351 itself (that is 1 + 3 + 9 + 13 + 27 + 39 + 117 = 209).

Parity of 351

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

Find out more:

What is an even number?

Is 351 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 351 is about 18.735.

Thus, the square root of 351 is not an integer, and therefore 351 is not a square number.

What is the square number of 351?

The square of a number (here 351) is the result of the product of this number (351) by itself (i.e., 351 × 351); the square of 351 is sometimes called "raising 351 to the power 2", or "351 squared".

The square of 351 is 123 201 because 351 × 351 = 351² = 123 201.

As a consequence, 351 is the square root of 123 201.

Number of digits of 351

351 is a number with 3 digits.

What are the multiples of 351?

The multiples of 351 are all integers evenly divisible by 351, that is all numbers such that the remainder of the division by 351 is zero. There are infinitely many multiples of 351. The smallest multiples of 351 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 351 too, since 0 × 351 = 0
351: indeed, 351 is a multiple of itself, since 351 is evenly divisible by 351 (we have 351 / 351 = 1, so the remainder of this division is indeed zero)
702: indeed, 702 = 351 × 2
1 053: indeed, 1 053 = 351 × 3
1 404: indeed, 1 404 = 351 × 4
1 755: indeed, 1 755 = 351 × 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 351). 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 18.735). 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 351

Preceding numbers: …349, 350
Following numbers: 352, 353…

Nearest numbers from 351

Preceding prime number: 349
Following prime number: 353