Is 336 a prime number?

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

For 336, the answer is: No, 336 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 336) is as follows: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336.

For 336 to be a prime number, it would have been required that 336 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

336 is a multiple of 1
336 is a multiple of 2
336 is a multiple of 3
336 is a multiple of 4
336 is a multiple of 6
336 is a multiple of 7
336 is a multiple of 8
336 is a multiple of 12
336 is a multiple of 14
336 is a multiple of 16
336 is a multiple of 21
336 is a multiple of 24
336 is a multiple of 28
336 is a multiple of 42
336 is a multiple of 48
336 is a multiple of 56
336 is a multiple of 84
336 is a multiple of 112
336 is a multiple of 168

For 336 to be a prime number, it would have been required that 336 has only two divisors, i.e., itself and 1.

Is 336 a deficient number?

No, 336 is not a deficient number: to be deficient, 336 should have been such that 336 is larger than the sum of its proper divisors, i.e., the divisors of 336 without 336 itself (that is 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 16 + 21 + 24 + 28 + 42 + 48 + 56 + 84 + 112 + 168 = 656).

In fact, 336 is an abundant number; 336 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 16 + 21 + 24 + 28 + 42 + 48 + 56 + 84 + 112 + 168 = 656). The smallest abundant number is 12.

Parity of 336

336 is an even number, because it is evenly divisible by 2: 336 / 2 = 168.

Find out more:

What is an even number?

Is 336 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 336 is about 18.330.

Thus, the square root of 336 is not an integer, and therefore 336 is not a square number.

What is the square number of 336?

The square of a number (here 336) is the result of the product of this number (336) by itself (i.e., 336 × 336); the square of 336 is sometimes called "raising 336 to the power 2", or "336 squared".

The square of 336 is 112 896 because 336 × 336 = 336² = 112 896.

As a consequence, 336 is the square root of 112 896.

Number of digits of 336

336 is a number with 3 digits.

What are the multiples of 336?

The multiples of 336 are all integers evenly divisible by 336, that is all numbers such that the remainder of the division by 336 is zero. There are infinitely many multiples of 336. The smallest multiples of 336 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 336 too, since 0 × 336 = 0
336: indeed, 336 is a multiple of itself, since 336 is evenly divisible by 336 (we have 336 / 336 = 1, so the remainder of this division is indeed zero)
672: indeed, 672 = 336 × 2
1 008: indeed, 1 008 = 336 × 3
1 344: indeed, 1 344 = 336 × 4
1 680: indeed, 1 680 = 336 × 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 336). 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 18.330). 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 336

Preceding numbers: …334, 335
Following numbers: 337, 338…

Nearest numbers from 336

Preceding prime number: 331
Following prime number: 337