Is 357 a prime number?

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

For 357, the answer is: No, 357 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 357) is as follows: 1, 3, 7, 17, 21, 51, 119, 357.

For 357 to be a prime number, it would have been required that 357 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

357 is a multiple of 1
357 is a multiple of 3
357 is a multiple of 7
357 is a multiple of 17
357 is a multiple of 21
357 is a multiple of 51
357 is a multiple of 119

For 357 to be a prime number, it would have been required that 357 has only two divisors, i.e., itself and 1.

Is 357 a deficient number?

Yes, 357 is a deficient number, that is to say 357 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 357 without 357 itself (that is 1 + 3 + 7 + 17 + 21 + 51 + 119 = 219).

Parity of 357

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

Find out more:

What is an even number?

Is 357 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 357 is about 18.894.

Thus, the square root of 357 is not an integer, and therefore 357 is not a square number.

What is the square number of 357?

The square of a number (here 357) is the result of the product of this number (357) by itself (i.e., 357 × 357); the square of 357 is sometimes called "raising 357 to the power 2", or "357 squared".

The square of 357 is 127 449 because 357 × 357 = 357² = 127 449.

As a consequence, 357 is the square root of 127 449.

Number of digits of 357

357 is a number with 3 digits.

What are the multiples of 357?

The multiples of 357 are all integers evenly divisible by 357, that is all numbers such that the remainder of the division by 357 is zero. There are infinitely many multiples of 357. The smallest multiples of 357 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 357 too, since 0 × 357 = 0
357: indeed, 357 is a multiple of itself, since 357 is evenly divisible by 357 (we have 357 / 357 = 1, so the remainder of this division is indeed zero)
714: indeed, 714 = 357 × 2
1 071: indeed, 1 071 = 357 × 3
1 428: indeed, 1 428 = 357 × 4
1 785: indeed, 1 785 = 357 × 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 357). 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 18.894). 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 357

Preceding numbers: …355, 356
Following numbers: 358, 359…

Nearest numbers from 357

Preceding prime number: 353
Following prime number: 359