Is 178 a prime number?

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

For 178, the answer is: No, 178 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 178) is as follows: 1, 2, 89, 178.

For 178 to be a prime number, it would have been required that 178 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

178 is a multiple of 1
178 is a multiple of 2
178 is a multiple of 89

For 178 to be a prime number, it would have been required that 178 has only two divisors, i.e., itself and 1.

However, 178 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 178 = 2 x 89, where 2 and 89 are both prime numbers.

Is 178 a deficient number?

Yes, 178 is a deficient number, that is to say 178 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 178 without 178 itself (that is 1 + 2 + 89 = 92).

Parity of 178

178 is an even number, because it is evenly divisible by 2: 178 / 2 = 89.

Find out more:

What is an even number?

Is 178 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 178 is about 13.342.

Thus, the square root of 178 is not an integer, and therefore 178 is not a square number.

What is the square number of 178?

The square of a number (here 178) is the result of the product of this number (178) by itself (i.e., 178 × 178); the square of 178 is sometimes called "raising 178 to the power 2", or "178 squared".

The square of 178 is 31 684 because 178 × 178 = 178² = 31 684.

As a consequence, 178 is the square root of 31 684.

Number of digits of 178

178 is a number with 3 digits.

What are the multiples of 178?

The multiples of 178 are all integers evenly divisible by 178, that is all numbers such that the remainder of the division by 178 is zero. There are infinitely many multiples of 178. The smallest multiples of 178 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 178 too, since 0 × 178 = 0
178: indeed, 178 is a multiple of itself, since 178 is evenly divisible by 178 (we have 178 / 178 = 1, so the remainder of this division is indeed zero)
356: indeed, 356 = 178 × 2
534: indeed, 534 = 178 × 3
712: indeed, 712 = 178 × 4
890: indeed, 890 = 178 × 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 178). 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 13.342). 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 178

Preceding numbers: …176, 177
Following numbers: 179, 180…

Nearest numbers from 178

Preceding prime number: 173
Following prime number: 179