Is 348 a prime number?

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

For 348, the answer is: No, 348 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 348) is as follows: 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348.

For 348 to be a prime number, it would have been required that 348 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

348 is a multiple of 1
348 is a multiple of 2
348 is a multiple of 3
348 is a multiple of 4
348 is a multiple of 6
348 is a multiple of 12
348 is a multiple of 29
348 is a multiple of 58
348 is a multiple of 87
348 is a multiple of 116
348 is a multiple of 174

For 348 to be a prime number, it would have been required that 348 has only two divisors, i.e., itself and 1.

Is 348 a deficient number?

No, 348 is not a deficient number: to be deficient, 348 should have been such that 348 is larger than the sum of its proper divisors, i.e., the divisors of 348 without 348 itself (that is 1 + 2 + 3 + 4 + 6 + 12 + 29 + 58 + 87 + 116 + 174 = 492).

In fact, 348 is an abundant number; 348 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 12 + 29 + 58 + 87 + 116 + 174 = 492). The smallest abundant number is 12.

Parity of 348

348 is an even number, because it is evenly divisible by 2: 348 / 2 = 174.

Find out more:

What is an even number?

Is 348 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 348 is about 18.655.

Thus, the square root of 348 is not an integer, and therefore 348 is not a square number.

What is the square number of 348?

The square of a number (here 348) is the result of the product of this number (348) by itself (i.e., 348 × 348); the square of 348 is sometimes called "raising 348 to the power 2", or "348 squared".

The square of 348 is 121 104 because 348 × 348 = 348² = 121 104.

As a consequence, 348 is the square root of 121 104.

Number of digits of 348

348 is a number with 3 digits.

What are the multiples of 348?

The multiples of 348 are all integers evenly divisible by 348, that is all numbers such that the remainder of the division by 348 is zero. There are infinitely many multiples of 348. The smallest multiples of 348 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 348 too, since 0 × 348 = 0
348: indeed, 348 is a multiple of itself, since 348 is evenly divisible by 348 (we have 348 / 348 = 1, so the remainder of this division is indeed zero)
696: indeed, 696 = 348 × 2
1 044: indeed, 1 044 = 348 × 3
1 392: indeed, 1 392 = 348 × 4
1 740: indeed, 1 740 = 348 × 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 348). 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 18.655). 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 348

Preceding numbers: …346, 347
Following numbers: 349, 350…

Nearest numbers from 348

Preceding prime number: 347
Following prime number: 349