Is 350 a prime number?

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

For 350, the answer is: No, 350 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 350) is as follows: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350.

For 350 to be a prime number, it would have been required that 350 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 350 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 350 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

350 is a multiple of 1
350 is a multiple of 2
350 is a multiple of 5
350 is a multiple of 7
350 is a multiple of 10
350 is a multiple of 14
350 is a multiple of 25
350 is a multiple of 35
350 is a multiple of 50
350 is a multiple of 70
350 is a multiple of 175

For 350 to be a prime number, it would have been required that 350 has only two divisors, i.e., itself and 1.

Is 350 a deficient number?

No, 350 is not a deficient number: to be deficient, 350 should have been such that 350 is larger than the sum of its proper divisors, i.e., the divisors of 350 without 350 itself (that is 1 + 2 + 5 + 7 + 10 + 14 + 25 + 35 + 50 + 70 + 175 = 394).

In fact, 350 is an abundant number; 350 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 5 + 7 + 10 + 14 + 25 + 35 + 50 + 70 + 175 = 394). The smallest abundant number is 12.

Parity of 350

350 is an even number, because it is evenly divisible by 2: 350 / 2 = 175.

Find out more:

What is an even number?

Is 350 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 350 is about 18.708.

Thus, the square root of 350 is not an integer, and therefore 350 is not a square number.

What is the square number of 350?

The square of a number (here 350) is the result of the product of this number (350) by itself (i.e., 350 × 350); the square of 350 is sometimes called "raising 350 to the power 2", or "350 squared".

The square of 350 is 122 500 because 350 × 350 = 350² = 122 500.

As a consequence, 350 is the square root of 122 500.

Number of digits of 350

350 is a number with 3 digits.

What are the multiples of 350?

The multiples of 350 are all integers evenly divisible by 350, that is all numbers such that the remainder of the division by 350 is zero. There are infinitely many multiples of 350. The smallest multiples of 350 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 350 too, since 0 × 350 = 0
350: indeed, 350 is a multiple of itself, since 350 is evenly divisible by 350 (we have 350 / 350 = 1, so the remainder of this division is indeed zero)
700: indeed, 700 = 350 × 2
1 050: indeed, 1 050 = 350 × 3
1 400: indeed, 1 400 = 350 × 4
1 750: indeed, 1 750 = 350 × 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 350). 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 18.708). 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 350

Preceding numbers: …348, 349
Following numbers: 351, 352…

Nearest numbers from 350

Preceding prime number: 349
Following prime number: 353