Is 174 a prime number?

The number 174 has got several factors, that are capable of dividing the number completely without leaving any remainder. Thus, the number 174 is a non-prime number. The factors of 174 include 1, 2, 3, 6, 29, 58, 87, and 174.

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. Here, 174 has more than 2 factors, hence making it a composite number.

Given below are a few ways that can be used to find prime or composite numbers.

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 to be checked whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 174 would simply be:

Divisors of 174 = 1, 2, 3, 6, 29, 58, 87, 174

Number of divisors = 8

The number 174 can be considered composite.
 

In the division test, we try to divide the number by any of the prime numbers. If we cannot, then it is considered a prime number.

In the divisibility method, the prime number only has 2 divisors, which are 1 and itself.

The divisors of 174 are 1, 2, 3, 6, 29, 58, 87, and 174.

Thus, 174 consists of 8 factors that divide it completely without any remainder.
 

The prime number chart is the list of prime numbers starting from 2 to infinity.

The list of prime numbers under 100 are;

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

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

This method is only used for a non-prime number/composite number. Since 174 is a composite number, the prime factorization for 174 is:

Factors of 174 = 2 × 3 × 29
 

• 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 distinct positive divisors. For example, 174, which can be divided by 1, 2, 3, 6, 29, 58, 87, and 174, is a composite number.

• Divisor: A number that divides another number completely without leaving a remainder. For example, the divisors of 174 are 1, 2, 3, 6, 29, 58, 87, and 174.

• Prime Factorization: The process of breaking down a number into the prime numbers that multiply together to form it. For 174, the prime factorization is 2 × 3 × 29.

• Divisibility Test: A method used to check if a number is divisible by another number. If a number divides evenly without leaving a remainder, then the number is divisible by it. For example, using divisibility tests helps determine if a number is prime or composite.