Summarize this article:
105 LearnersLast updated on September 24, 2025
GCF of 162 and 192
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 162 and 192.
What is the GCF of 162 and 192?
The greatest common factor of 162 and 192 is 6. The largest divisor of two or more numbers is called the GCF of the numbers.
If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.
The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 162 and 192?
To find the GCF of 162 and 192, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 162 and 192 by Using Listing of Factors
Steps to find the GCF of 162 and 192 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 162 = 1, 2, 3, 6, 9, 18, 27, 54, 81, 162.
Factors of 192 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
Step 2: Now, identify the common factors of them Common factors of 162 and 192: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6.
The GCF of 162 and 192 is 6.
GCF of 162 and 192 Using Prime Factorization
To find the GCF of 162 and 192 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime factors of 162: 162 = 2 x 3 x 3 x 3 x 3 = 2 x 34
Prime factors of 192: 192 = 2 x 2 x 2 x 2 x 2 x 3 = 26 x 3
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 3
Step 3: Multiply the common prime factors 2 x 3 = 6.
The Greatest Common Factor of 162 and 192 is 6.
GCF of 162 and 192 Using Division Method or Euclidean Algorithm Method
Find the GCF of 162 and 192 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 192 by 162 192 ÷ 162 = 1 (quotient), The remainder is calculated as 192 − (162×1) = 30
The remainder is 30, not zero, so continue the process
Step 2: Now divide the previous divisor (162) by the previous remainder (30) Divide 162 by 30 162 ÷ 30 = 5 (quotient), remainder = 162 − (30×5) = 12
Step 3: Now divide the previous divisor (30) by the previous remainder (12) 30 ÷ 12 = 2 (quotient), remainder = 30 − (12×2) = 6
Step 4: Now divide the previous divisor (12) by the previous remainder (6) 12 ÷ 6 = 2 (quotient), remainder = 12 − (6×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 162 and 192 is 6.
Common Mistakes and How to Avoid Them in GCF of 162 and 192
Finding the GCF of 162 and 192 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 162, students may mention 5, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors and multiples. In that confusion, sometimes they may write multiples instead of factors.
To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true, as a GCF can also be an odd number.
To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 162 and 192 Examples
Problem 1
A baker has 162 chocolate chips and 192 sprinkles. She wants to make as many identical cookies as possible, using the largest possible number of chips and sprinkles in each cookie. How many chips and sprinkles will be in each cookie?
We should find the GCF of 162 and 192. GCF of 162 and 192 2 x 3 = 6.
There are 6 identical cookies. 162 ÷ 6 = 27 192 ÷ 6 = 32
Each cookie will have 27 chocolate chips and 32 sprinkles.
Explanation
As the GCF of 162 and 192 is 6, the baker can make 6 cookies.
Now divide 162 and 192 by 6. Each cookie gets 27 chocolate chips and 32 sprinkles.
Problem 2
A music teacher has 162 drums and 192 tambourines. They want to arrange them in rows with the same number of instruments in each row, using the largest possible number of instruments per row. How many instruments will be in each row?
GCF of 162 and 192 2 x 3 = 6.
So each row will have 6 instruments.
Explanation
There are 162 drums and 192 tambourines. To find the total number of instruments in each row, we should find the GCF of 162 and 192. There will be 6 instruments in each row.
Problem 3
A seamstress has 162 meters of silk fabric and 192 meters of cotton fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 162 and 192. The GCF of 162 and 192 2 x 3 = 6. The fabric is 6 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 162 and 192, which is 6. The length of each piece of fabric will be 6 meters.
Problem 4
A carpenter has two wooden planks, one 162 cm long and the other 192 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood. GCF of 162 and 192 2 x 3 = 6.
The longest length of each piece is 6 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 162 cm and 192 cm, respectively, we have to find the GCF of 162 and 192, which is 6 cm. The longest length of each piece is 6 cm.
Problem 5
If the GCF of 162 and ‘b’ is 6, and the LCM is 5184, find ‘b’.
The value of ‘b’ is 192.
Explanation
GCF x LCM = product of the numbers
6 x 5184 = 162 x b
31104 = 162b
b = 31104 ÷ 162 = 192
FAQs on the Greatest Common Factor of 162 and 192
1.What is the LCM of 162 and 192?
2.Is 162 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 192?
5.Are 162 and 192 prime numbers?
Important Glossaries for GCF of 162 and 192
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 15 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5, and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed the LCM. For example, the LCM of 24 and 36 is 72.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 162 and 192
![Important Math Links Icon]()
Next to GCF of 162 and 192
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.
