Is 177 a Prime Number?

Since 177 has 4 factors, it is not a prime number. The basic methods to check if a number is prime are the counting divisors method, divisibility method, prime number chart, and prime factorization.

This method will find the total number of divisors of the given number.  If there are more than two divisors, then the given number is composite, not prime.

The divisors of 177 = 1, 3, 59, 177

Therefore, 177 is not prime.
 

The divisibility method determines whether a number is composite or not. Make use of the divisibility rule of 2 (if the number is even), the divisibility rule of 3 (if the sum of digits is a multiple of 3), and so on.  The number 177 is divisible by 3, we use the divisibility rule of 3. Hence, factors of 177 are 1, 3, 59, and 177.
 

This method will check if a number is prime or not with the help of a prime number chart. Only if the number is seen in the chart, then it's a prime.
 

Prime Factorization expresses the product of prime factors of composite numbers in exponential form. The prime factors of 177 are 3 and 59. 
The prime factorization of 177 → 3¹ × 59¹
 

• Prime Number: Natural number with two factors. For example, numbers like 91, 101, 311, etc.

• Composite Number: Numbers with more than two factors. For example, numbers like 84, 93, 115, 162, and so on.

• Prime Factorization: Method to express the product of prime factors using exponents.