It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 179, the answer is: yes, 179 is a prime number because it has only two distinct divisors: 1 and itself (179).
As a consequence, 179 is only a multiple of 1 and 179..
Since 179 is a prime number, 179 is also a deficient number, that is to say 179 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 179 without 179 itself (that is 1, by definition!).
Parity of 179
179 is an odd number, because it is not evenly divisible by 2.
Is 179 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 179 is about 13.379.
Thus, the square root of 179 is not an integer, and therefore 179 is not a square number.
Anyway, 179 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 179?
The square of a number (here 179) is the result of the product of this number (179) by itself (i.e., 179 × 179); the square of 179 is sometimes called "raising 179 to the power 2", or "179 squared".
As a consequence, 179 is the square root of 32 041.
Number of digits of 179
179 is a number with 3 digits.
What are the multiples of 179?
The multiples of 179 are all integers evenly divisible by 179, that is all numbers such that the remainder of the division by 179 is zero. There are infinitely many multiples of 179. The smallest multiples of 179 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 179 too, since 0 × 179 = 0
- 179: indeed, 179 is a multiple of itself, since 179 is evenly divisible by 179 (we have 179 / 179 = 1, so the remainder of this division is indeed zero)
- 358: indeed, 358 = 179 × 2
- 537: indeed, 537 = 179 × 3
- 716: indeed, 716 = 179 × 4
- 895: indeed, 895 = 179 × 5
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 179). 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 13.379). 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.