Is 345 a prime number?

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

For 345, the answer is: No, 345 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 345) is as follows: 1, 3, 5, 15, 23, 69, 115, 345.

For 345 to be a prime number, it would have been required that 345 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 345 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 345 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

345 is a multiple of 1
345 is a multiple of 3
345 is a multiple of 5
345 is a multiple of 15
345 is a multiple of 23
345 is a multiple of 69
345 is a multiple of 115

For 345 to be a prime number, it would have been required that 345 has only two divisors, i.e., itself and 1.

Is 345 a deficient number?

Yes, 345 is a deficient number, that is to say 345 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 345 without 345 itself (that is 1 + 3 + 5 + 15 + 23 + 69 + 115 = 231).

Parity of 345

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

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What is an even number?

Is 345 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 345 is about 18.574.

Thus, the square root of 345 is not an integer, and therefore 345 is not a square number.

What is the square number of 345?

The square of a number (here 345) is the result of the product of this number (345) by itself (i.e., 345 × 345); the square of 345 is sometimes called "raising 345 to the power 2", or "345 squared".

The square of 345 is 119 025 because 345 × 345 = 345² = 119 025.

As a consequence, 345 is the square root of 119 025.

Number of digits of 345

345 is a number with 3 digits.

What are the multiples of 345?

The multiples of 345 are all integers evenly divisible by 345, that is all numbers such that the remainder of the division by 345 is zero. There are infinitely many multiples of 345. The smallest multiples of 345 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 345 too, since 0 × 345 = 0
345: indeed, 345 is a multiple of itself, since 345 is evenly divisible by 345 (we have 345 / 345 = 1, so the remainder of this division is indeed zero)
690: indeed, 690 = 345 × 2
1 035: indeed, 1 035 = 345 × 3
1 380: indeed, 1 380 = 345 × 4
1 725: indeed, 1 725 = 345 × 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 345). 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 18.574). 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 345

Preceding numbers: …343, 344
Following numbers: 346, 347…

Nearest numbers from 345

Preceding prime number: 337
Following prime number: 347