Is 172 a prime number?

The number 172 has multiple factors that can divide it completely without leaving any remainder. Thus, the number 172 is a non-prime number. The factors of 172 include 1, 2, 4, 43, 86, and 172.

For a number to be a prime number, it should have exactly 2 factors: 1 and the number itself. Since 172 has more than 2 factors, it is categorized as a composite number.

Given below are a few methods that can be used to determine whether a number is prime or composite.
The different methods we can use to check if a number is a prime number are explained below:

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. Prime Factorization
    

For the counting divisors method, it is necessary to check whether the number is divisible by any numbers other than 1 and itself.

The counting divisors method for 172 would simply be:

• Divisors of 172 = 1, 2, 4, 43, 86, 172
• Number of divisors = 6

Since the number 172 has more than 2 divisors, it can be considered composite.
 

In the divisibility test, we try to divide the number by smaller prime numbers. If it is divisible, then it is considered a non-prime number.

For 172:

Divisors of 172 = 1, 2, 4, 43, 86, 172

Thus, 172 consists of 6 factors that divide it completely without any remainder, confirming it is not a prime number.
 

The prime number chart lists prime numbers starting from 2 to infinity.

The list of prime numbers under 200 includes:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

Since 172 is not present in the list, it is not a prime number.
 

This method is used for non-prime or composite numbers. Since 172 is a composite number, the prime factorization for 172 is:

• Factors of 172 = 2×2×43

• Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For example, 2, 3, and 5 are prime numbers.

• Composite Number: A natural number greater than 1 that has more than two positive divisors. For instance, 4, 6, and 8 are composite numbers.

• Divisibility Test: A method used to determine if one number can divide another completely, leaving no remainder. It is commonly applied to check a number's factors.

• Prime Factorization: The process of expressing a number as a product of its prime factors. For example, 28 can be written as 2×2×7

• Factors: Numbers that divide another number completely without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.