214 LearnersLast updated on May 26th, 2025
Factors Of 172
A number that can divide another number evenly without leaving any remainder is called a factor. Factors are useful in many real-life situations, such as construction, where it is used to determine the dimensions of materials to avoid waste. Next, let's discuss the factors of 172.
What are the Factors of 172?
Prime numbers can have just two factors, which are 1 and the number itself. Composite numbers have more than two factors. Now, let us learn more about the factors of 172.
Negative factors of 172: -1, -2, -4, -43, -86, and -172.
Prime factors of 172: 2 and 43.
Prime factorization of 172: 22 × 431
The sum of factors of 172: 1 + 2 + 4 + 43 + 86 + 172 = 308
How to Find the Factors of 172?
For finding factors, school kids use different methods for easy calculation. A few commonly used methods are as follows:
- Use of Multiplication Method
- Use of Division Method
- Use of Prime Factors and Prime Factorization.
So, here we discuss a detailed explanation of the following methods:
Finding Factors Using Multiplication Method
So in the multiplication method, we will try to find out what numbers will multiply together, and give us the value 172. We will check the factors step by step:
Step 1: Start to multiply with numbers, which gives the value of 172.
Start with 1, and continue to multiply with other numbers.
1 × 172 = 172
2 × 86 = 172
4 × 43 = 172
Step 2: After the calculation, we get these numbers, the factors of 172.
Step 3: The positive factor pairs of 172 found through multiplication are (1, 172), (2, 86), (4, 43)
Step 4: The negative factor pairs of 172 are (-1, -2), (-4, -43), (-86, -172).
Finding Factors Using Division Method
Using this method we will break down the given number till our remainder is zero. Let us go through the step-by-step process to find the factors of 172:
Step 1: Divide 172 by smaller numbers and see if there is any remainder. E.g., 172/1 = 172.
Step 2: We will continue in the same way and check for other numbers as well. For 172, the factors are 1, 2, 4, 43, 86, and 172. Because 172 can be divided evenly by these numbers.
172 ÷ 2 =86
172 ÷ 4 =43
172 ÷ 43=4
172 ÷ 172=1
Prime Factors and Prime Factorization
The prime factors of 172 are 2 and 43. The prime factors can be found using the methods given below:
- Prime Factorization
- Factor Tree
By Using Prime Factorization: When using this method, the number is divided by its prime numbers until it is factored completely.
2 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.
172 ÷ 2 = 86
86 ÷ 2 = 43
The prime factorization of 172 is :
172 = 22 × 43
Finally, using the prime factorization method, the prime factors of 172 are 2 and 43.
Using Factor Tree
A factor tree is a visual representation of breaking a number into its prime factors. It is an easy and simple way to present the factors.
Step 1: 172 divided by 2 gives us the answer 86
Step 2: Since 86 is not a prime number, it can be divided further.
The prime factorization of 172 is written below :
172 = 22 × 43
Factor Pairs Of 172
Every number has either a positive or negative factor. Let us look at those sets of factors.
Positive pair Factors:(1, 172), (2, 86), (4, 43)
Negative pair Factors: (-1, -2), (-4, -43), (-86, -172).
Common Mistakes and How to Avoid Them While Solving Factors Of 172
Children tend to make mistakes while finding the factors of a number. Let us look at how to avoid those mistakes.
Mistake 1
Confusing Factors with Multiples
The factors can divide a number exactly, whereas multiples are the product of multiplying the number by whole numbers. For example for 12, the factors are 1, 2, 3, 4, 6, and 12. And the multiples are 12, 24, and 36, etc… To avoid this confusion, always understand the concept separately.
Factors Of 172 Examples
Problem 1
What is the LCM and GCF of 172 and 120?
The LCM of 172 and 120 is 5160, and the GCF of 172 and 120 is 4.
Explanation
The LCM is the least common multiple of both numbers, whereas the greatest common factor is the largest number that can be divided by both 172 and 120, without any remainder. The step-by-step calculation is :
Step 1: Find prime factorization of 172 and 120
Prime factors of 172 = 22 × 43
Prime factors of 120 = 23 × 3 × 5
GCF is the lowest power of all common prime factors.
GCF = 22 = 4
LCM is the highest power of each prime factor present in both numbers.
LCM = 23 × 3 1 × 51 = 5160.
Problem 2
A garden fence is 172 meters long. Can it be divided into 2-meter sections?
Yes, 86 sections.
Explanation
Yes, the garden fence can be divided into 2-meter sections. 172 ÷ 2 equals 86, with no leftovers. So, 2 is a factor of 172. There are 86 sections.
Problem 3
Hana has a small library in her home. She plans to arrange the library room. The library has 172 identical books on a certain topic. She wants to place these books equally on 4 different shelves. How many books will each shelf hold?
She can arrange 43 books held on each shelf.
Explanation
The easy way she can arrange the book is, to calculate the number of books each shelf will hold, and divide the total number of books by the total number of shelves.
No. of books = 172
No. of shelves = 4
Divide 172 by 4: 172÷ 4 = 43.
Therefore, each shelf will hold 43 books.
FAQs on Factors Of 172
1.Find the factor pairs of 172.
2.Is 172 a perfect square?
3.What are the factors of 172?
4.Does 173 have any factors?
5.What is the factor of 72?
Important Glossaries For Factors Of 172
- Factors: The factors of numbers are complete numbers, that can be divided into another number evenly without remainder. Like 6 is divisible by 1, 2, 3, and 6, therefore, 1, 2, 3, and 6 are the factors of 6.
- Prime Factors: Prime numbers that multiply together to give a certain product. For 172 the prime factors are 2 and 43.
- Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).
Explore More numbers
Previous to Factors Of 172
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.
