Is 342 a prime number?

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

For 342, the answer is: No, 342 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 342) is as follows: 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342.

For 342 to be a prime number, it would have been required that 342 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

342 is a multiple of 1
342 is a multiple of 2
342 is a multiple of 3
342 is a multiple of 6
342 is a multiple of 9
342 is a multiple of 18
342 is a multiple of 19
342 is a multiple of 38
342 is a multiple of 57
342 is a multiple of 114
342 is a multiple of 171

For 342 to be a prime number, it would have been required that 342 has only two divisors, i.e., itself and 1.

Is 342 a deficient number?

No, 342 is not a deficient number: to be deficient, 342 should have been such that 342 is larger than the sum of its proper divisors, i.e., the divisors of 342 without 342 itself (that is 1 + 2 + 3 + 6 + 9 + 18 + 19 + 38 + 57 + 114 + 171 = 438).

In fact, 342 is an abundant number; 342 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 + 18 + 19 + 38 + 57 + 114 + 171 = 438). The smallest abundant number is 12.

Parity of 342

342 is an even number, because it is evenly divisible by 2: 342 / 2 = 171.

Find out more:

What is an even number?

Is 342 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 342 is about 18.493.

Thus, the square root of 342 is not an integer, and therefore 342 is not a square number.

What is the square number of 342?

The square of a number (here 342) is the result of the product of this number (342) by itself (i.e., 342 × 342); the square of 342 is sometimes called "raising 342 to the power 2", or "342 squared".

The square of 342 is 116 964 because 342 × 342 = 342² = 116 964.

As a consequence, 342 is the square root of 116 964.

Number of digits of 342

342 is a number with 3 digits.

What are the multiples of 342?

The multiples of 342 are all integers evenly divisible by 342, that is all numbers such that the remainder of the division by 342 is zero. There are infinitely many multiples of 342. The smallest multiples of 342 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 342 too, since 0 × 342 = 0
342: indeed, 342 is a multiple of itself, since 342 is evenly divisible by 342 (we have 342 / 342 = 1, so the remainder of this division is indeed zero)
684: indeed, 684 = 342 × 2
1 026: indeed, 1 026 = 342 × 3
1 368: indeed, 1 368 = 342 × 4
1 710: indeed, 1 710 = 342 × 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 342). 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 18.493). 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 342

Preceding numbers: …340, 341
Following numbers: 343, 344…

Nearest numbers from 342

Preceding prime number: 337
Following prime number: 347