Is 177 a prime number?

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

For 177, the answer is: No, 177 is not a prime number.

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

For 177 to be a prime number, it would have been required that 177 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

177 is a multiple of 1
177 is a multiple of 3
177 is a multiple of 59

For 177 to be a prime number, it would have been required that 177 has only two divisors, i.e., itself and 1.

However, 177 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 177 = 3 x 59, where 3 and 59 are both prime numbers.

Is 177 a deficient number?

Yes, 177 is a deficient number, that is to say 177 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 177 without 177 itself (that is 1 + 3 + 59 = 63).

Parity of 177

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

Find out more:

What is an even number?

Is 177 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 177 is about 13.304.

Thus, the square root of 177 is not an integer, and therefore 177 is not a square number.

What is the square number of 177?

The square of a number (here 177) is the result of the product of this number (177) by itself (i.e., 177 × 177); the square of 177 is sometimes called "raising 177 to the power 2", or "177 squared".

The square of 177 is 31 329 because 177 × 177 = 177² = 31 329.

As a consequence, 177 is the square root of 31 329.

Number of digits of 177

177 is a number with 3 digits.

What are the multiples of 177?

The multiples of 177 are all integers evenly divisible by 177, that is all numbers such that the remainder of the division by 177 is zero. There are infinitely many multiples of 177. The smallest multiples of 177 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 177 too, since 0 × 177 = 0
177: indeed, 177 is a multiple of itself, since 177 is evenly divisible by 177 (we have 177 / 177 = 1, so the remainder of this division is indeed zero)
354: indeed, 354 = 177 × 2
531: indeed, 531 = 177 × 3
708: indeed, 708 = 177 × 4
885: indeed, 885 = 177 × 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 177). 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 13.304). 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 177

Preceding numbers: …175, 176
Following numbers: 178, 179…

Nearest numbers from 177

Preceding prime number: 173
Following prime number: 179