Factors of 171
2026-02-28 12:41 Diff
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Last updated on December 11, 2025

In this topic, let's learn about factors. It is scarce to find numbers that will divide a given number up to the smallest unit without remainder. These numbers are known as the factors, and learning about factors happens when a student comes across a number or number pair in the real world.

What are the factors of 171?

With the help of the long division method, we can find out that 171 can be easily divided by 1, 3, 9, 19, 57, and 171. It is also worth remembering that numbers, having only 2 factors, are called prime numbers.
 

How to find the factors of 171

There are many methods which the students can use to find out the factors of a number. Some of the most used methods are given below.

  • Multiplication method
  • Division method
  • Factor tree

Finding factors using multiplication method

Multiplication method is quite an easy method where we find the pair of numbers which when multiplied with each other give the desired number. For 208 the pairs are.


1×171=171


3×57=171


9×19=171


Hence, we can conclude that the factors of 171 are 1, 3, 9, 19, 57, and 171
 

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Finding factors by division method

In the division method, you need to divide the given number 208 by every number starting from 1. If any number is able to divide it without leaving any reminder, then that number is considered as one of its factors.


171÷1=171 (no remainder)


171÷3=57 (no remainder)


171÷9=19 (no remainder)


171÷19=9 (no remainder)
 

Prime factors and prime factorization

Prime factorization is done by dividing the number by prime numbers to see which prime number is able to divide it, and if it does, then that number is considered as a prime number.


171÷3= 57 (2 is a prime factor).


19 is also prime.


Therefore, prime factors of 171 are 3 and 19
 

Factor tree

A factor tree is a form of number tree, which is a diagram which represents simple division, where the number at the top is divided until it reaches a prime number or cannot be further divided.

Common mistakes and how to avoid them in factors of 171.

It is quite normal for students to commit a few mistakes while trying to find out the factors of a number. Below are a few such mistakes and how to avoid them.

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Problem 1

What is the greatest common factor (GCF) of 18 and 24?

Okay, lets begin

6
 

Explanation

Factors of 18: 1, 2, 3, 6, 9, 18


Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24


GCF: 6

Well explained 👍

Problem 2

What are the prime factors of 84?

Okay, lets begin

22 × 3 × 7
 

Explanation

84 ÷ 2 = 42


42 ÷ 2 = 21


21 ÷ 3 = 7
 

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Problem 3

If a number has exactly 4 factors, what could it be?

Okay, lets begin

The answer is going to be 6
 

Explanation

6 has 4 factors, this can be proved by listing its factors: 1, 2, 3, 6


A number with 4 factors is often the product of two distinct prime numbers.


Here, 6 is the product of 3 and 2.
 

Well explained 👍

FAQs on factors of 171

1. How many composite factors does 171 have?

By applying the division method on 171 we get to know that the numbers 1,3,9,19,57,171 are the factors of 171, among which 1, 3 and 19 are prime numbers. Hence, the composite factors of 171 are 9, 57, 171.
 

2.How many factors do prime numbers have?

According to the prime number definition, a number with only two distinct divisors or factors are known as prime numbers, and they must not have any prime factors of their own.
 

3.What is the largest factor of 171?

So for the number 171 the largest factor which is able to divide it, and leaves no remainder is 171 itself, therefore the largest factor of the number 171 is the number 171 itself.
 

4. Can 1 be a factor of all the numbers?

Yes, because on division the number divided by one gives the same number and there is no remainder left after division.
 

5.Is 171 a composite number?

 A number that can only be split by two distinct divisors is a prime number, 171 has over two divisors, so it’s a non-prime also known as a composite number.
 

Important glossaries for factors of 208

  • Divisor: Any integer that can be divided, with no remainder, by some other integer, is a divisor.
  • Prime Factorization: Writing a number as the product of its own prime factors.
  • Factor Pair: Multiplication of two factors to get a product.
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.