# Factors of 171

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

#### How to find factors of a number

 1.   Find factors of 171 using Division Method 2.   Find factors of 171 using Prime Factorization 3.   Find factors of 171 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 171

• Divide 171 by 1: 171 ÷ 1 : Remainder = 0
• Divide 171 by 3: 171 ÷ 3 : Remainder = 0
• Divide 171 by 9: 171 ÷ 9 : Remainder = 0
• Divide 171 by 19: 171 ÷ 19 : Remainder = 0
• Divide 171 by 57: 171 ÷ 57 : Remainder = 0
• Divide 171 by 171: 171 ÷ 171 : Remainder = 0

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

#### 2. Steps to find factors of 171 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 171 using the division method, follow these steps:

• Step 1. Start dividing 171 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 171, which is 3. Divide 171 by 3 to obtain the quotient (57).
171 ÷ 3 = 57
• Step 3. Repeat step 1 with the obtained quotient (57).
57 ÷ 3 = 19
19 ÷ 19 = 1

So, the prime factorization of 171 is, 171 = 3 x 3 x 19.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 171 as shown below:

So, the prime factorization of 171 is, 171 = 3 x 3 x 19.

#### 3. Find factors of 171 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 171 would be the two numbers which, when multiplied, give 171 as the result.

The following table represents the calculation of factors of 171 in pairs:

Factor Pair Pair Factorization
1 and 171 1 x 171 = 171
3 and 57 3 x 57 = 171
9 and 19 9 x 19 = 171

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 171. They are called negative pair factors.

Hence, the negative pairs of 171 would be ( -1 , -171 ) , ( -3 , -57 ) and ( -9 , -19 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 171 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 3, 9, 19, 57, 171 are exact divisors of 171.
• Factors of 171 are 1, 3, 9, 19, 57, 171. Each factor divides 171 without leaving a remainder.

• Which is the smallest prime factor of 171?

Smallest prime factor of 171 is 3.

• Is 171 a perfect square?

No 171 is not a perfect square.

• What are five multiples of 171?

First five multiples of 171 are 342, 513, 684, 855, 1026.

• What is prime factorization of 171?

Prime factorization of 171 is 3 x 3 x 19.

• What are factors of 171?

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

• How do you find factors of a negative number? ( eg. -171 )?

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

• Is 171 a whole number?

Yes 171 is a whole number.

• Which is greatest factor of 171?

The greatest factor of 171 is 57.

• What are the prime factors of 171?

The factors of 171 are 1, 3, 9, 19, 57, 171.
Prime factors of 171 are 3, 3, 19.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 171. Can you help her?

Prime factors of 171 are 3, 3, 19.
Hence, the product of prime factors of 57.

Can you help Rubel to find out the product of the even factors of 171?

Factors of 171 are 1, 3, 9, 19, 57, 171.
Even factors of 171 are 0.
Hence, product of even factors of 171 is; 0 = 0.

Joy wants to calculate mean of all the factors of 171. Help him in finding the mean of 171.

Factors of 171 are 1, 3, 9, 19, 57, 171.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 171 is 1 + 3 + 9 + 19 + 57 + 171 = 260.
Hence, the mean of factors of 171 is 260 ÷ 6 = 43.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 171? Help her in writing all the factors.

Positive factors are 1, 3, 9, 19, 57, 171.
Negative factors are -1, -3, -9, -19, -57, -171.

How many factors are there for 171?

Factors of 171 are 1, 3, 9, 19, 57, 171.
So there are in total 6 factors.

Joey wants to write all the prime factors of 171 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 171 are 3, 3, 19.
So in exponential form it can be written as 32 x 19.

Kevin has been asked to write 5 factor(s) of 171. Can you predict the answer?

5 factor(s) of 171 are 1, 3, 9, 19, 57.