Factors of 171: Prime Factorization, Methods, and Examples

Number 171 can be fully divided by 1, 3, 9, 19, 57, and 171 completely without leaving any remainder.

All these numbers are termed as factors of 171. The factors of the given number can be positive as well as negative provided that the given number is achieved upon multiplication of two-factor integers.

Factors of 171

Here are the factors of number 171.

Factors of 171: 1, 3, 9, 19, 57, 171

Negative Factors of 171

The negative factors of 171 are similar to its positive factors, just with a negative sign.

Negative Factors of 171: -1, -3, -9, -19, -57, -171

Prime Factorization of 171

The prime factorization of 171 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 3 x 19

In this article, we will learn about the factors of 171 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 171?

The factors of 171 are 1, 3, 9, 19, 57, and 171. All of these numbers are the factors as they do not leave any remainder when divided by 171.

The factors of 171 are classified as prime numbers and composite numbers. The prime factors of the number 171 can be determined using the technique of prime factorization.

How To Find the Factors of 171?

You can find the factors of 171 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 171, create a list containing the numbers that are exactly divisible by 171 with zero remainders. One important thing to note is that 1 and 171 are the 171’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 171 are determined as follows:

\[\dfrac{171}{1} = 171\]

\[\dfrac{171}{3} = 57\]

\[\dfrac{171}{9} = 19\]

\[\dfrac{171}{171} = 1\]

The divisors, as well as the quotients, are called the factors of 171. Therefore, 1, 3, 9, 19, 57, and 171. are the factors of 171.

Total Number of Factors of 171

For 171 there are 6 positive factors and 6 negative ones. So in total, there are m factors of 171. 

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure the total number of factors of 171 is given as:

Factorization of 171 is 1 x $3^2$ x 19.

The exponent of 1 and 19 is 1. The exponent of 3 is 2.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 171 is 12. 6 are positive and 6 factors are negative.

Important Notes

Here are some important points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 171 by Prime Factorization

The number 171 is a composite. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 171 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 171, start dividing by its smallest prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 171 can be expressed as:

171 = $3^2$ x 19

Factors of 171 in Pairs

The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Factor pairs can be more than one depending on the total number of factors of the given numbers.

For 171, the factor pairs can be found as:

1 x 171 = 171 

3 x 57 = 171

9 x 19 = 171 

The possible factor pairs of 171 are given as (1, 171), (3, 57), and (9, 19 ).

All these numbers in pairs, when multiplied, give 171 as the product.

The negative factor pairs of X are given as:

-1 x -171 = 171 

-3 x -57 = 171 

-9 x -19 = 171 

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign due to which the resulting product is the original positive number. Therefore, -1, -3, -9, -19, -57, and -171 are called negative factors of 171.

The list of all the factors of 171 including positive as well as negative numbers is given below.

Factor list of 171: 1, -1, 3, -3, 9, -9, 19, -19, 57, -57, 171, and -171

Factors of 171 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 171 are there?

Solution

The total number of Factors of 171 is 6.

Factors of 171 are 1, 3, 9, 19, 57, and 171.

Example 2

Find the factors of 171 using prime factorization.

Solution

The prime factorization of 171 is given as:

171 $\div$ 3 = 57 

57 $\div$ 3 = 19 

19 $\div$ 19 = 1 

So the prime factorization of 171 can be written as:

$3^2$ x 19 = 171 

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