Is 343 a prime number?

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

For 343, the answer is: No, 343 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 343) is as follows: 1, 7, 49, 343.

For 343 to be a prime number, it would have been required that 343 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

343 is a multiple of 1
343 is a multiple of 7
343 is a multiple of 49

For 343 to be a prime number, it would have been required that 343 has only two divisors, i.e., itself and 1.

Is 343 a deficient number?

Yes, 343 is a deficient number, that is to say 343 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 343 without 343 itself (that is 1 + 7 + 49 = 57).

Parity of 343

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

Find out more:

What is an even number?

Is 343 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 343 is about 18.520.

Thus, the square root of 343 is not an integer, and therefore 343 is not a square number.

What is the square number of 343?

The square of a number (here 343) is the result of the product of this number (343) by itself (i.e., 343 × 343); the square of 343 is sometimes called "raising 343 to the power 2", or "343 squared".

The square of 343 is 117 649 because 343 × 343 = 343² = 117 649.

As a consequence, 343 is the square root of 117 649.

Number of digits of 343

343 is a number with 3 digits.

What are the multiples of 343?

The multiples of 343 are all integers evenly divisible by 343, that is all numbers such that the remainder of the division by 343 is zero. There are infinitely many multiples of 343. The smallest multiples of 343 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 343 too, since 0 × 343 = 0
343: indeed, 343 is a multiple of itself, since 343 is evenly divisible by 343 (we have 343 / 343 = 1, so the remainder of this division is indeed zero)
686: indeed, 686 = 343 × 2
1 029: indeed, 1 029 = 343 × 3
1 372: indeed, 1 372 = 343 × 4
1 715: indeed, 1 715 = 343 × 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 343). 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 18.520). 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 343

Preceding numbers: …341, 342
Following numbers: 344, 345…

Nearest numbers from 343

Preceding prime number: 337
Following prime number: 347