Is 354 a prime number?

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

For 354, the answer is: No, 354 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 354) is as follows: 1, 2, 3, 6, 59, 118, 177, 354.

For 354 to be a prime number, it would have been required that 354 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

354 is a multiple of 1
354 is a multiple of 2
354 is a multiple of 3
354 is a multiple of 6
354 is a multiple of 59
354 is a multiple of 118
354 is a multiple of 177

For 354 to be a prime number, it would have been required that 354 has only two divisors, i.e., itself and 1.

Is 354 a deficient number?

No, 354 is not a deficient number: to be deficient, 354 should have been such that 354 is larger than the sum of its proper divisors, i.e., the divisors of 354 without 354 itself (that is 1 + 2 + 3 + 6 + 59 + 118 + 177 = 366).

In fact, 354 is an abundant number; 354 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 59 + 118 + 177 = 366). The smallest abundant number is 12.

Parity of 354

354 is an even number, because it is evenly divisible by 2: 354 / 2 = 177.

Find out more:

What is an even number?

Is 354 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 354 is about 18.815.

Thus, the square root of 354 is not an integer, and therefore 354 is not a square number.

What is the square number of 354?

The square of a number (here 354) is the result of the product of this number (354) by itself (i.e., 354 × 354); the square of 354 is sometimes called "raising 354 to the power 2", or "354 squared".

The square of 354 is 125 316 because 354 × 354 = 354² = 125 316.

As a consequence, 354 is the square root of 125 316.

Number of digits of 354

354 is a number with 3 digits.

What are the multiples of 354?

The multiples of 354 are all integers evenly divisible by 354, that is all numbers such that the remainder of the division by 354 is zero. There are infinitely many multiples of 354. The smallest multiples of 354 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 354 too, since 0 × 354 = 0
354: indeed, 354 is a multiple of itself, since 354 is evenly divisible by 354 (we have 354 / 354 = 1, so the remainder of this division is indeed zero)
708: indeed, 708 = 354 × 2
1 062: indeed, 1 062 = 354 × 3
1 416: indeed, 1 416 = 354 × 4
1 770: indeed, 1 770 = 354 × 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 354). 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 18.815). 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 354

Preceding numbers: …352, 353
Following numbers: 355, 356…

Nearest numbers from 354

Preceding prime number: 353
Following prime number: 359