105 LearnersLast updated on August 5th, 2025
GCF of 12 and 162
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 12 and 162.
What is the GCF of 12 and 162?
The greatest common factor of 12 and 162 is 6. The largest divisor of two or more numbers is called the GCF of the number. 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, which are always positive.
How to find the GCF of 12 and 162?
To find the GCF of 12 and 162, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 12 and 162 by Using Listing of Factors
Steps to find the GCF of 12 and 162 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 12 = 1, 2, 3, 4, 6, 12.
Factors of 162 = 1, 2, 3, 6, 9, 18, 27, 54, 81, 162.
Step 2: Now, identify the common factors of them
Common factors of 12 and 162: 1, 2, 3, 6.
Step 3: Choose the largest factor
The largest factor that both numbers have is 6.
The GCF of 12 and 162 is 6.
GCF of 12 and 162 Using Prime Factorization
To find the GCF of 12 and 162 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 12: 12 = 2 x 2 x 3 = 2² x 3
Prime Factors of 162: 162 = 2 x 3 x 3 x 3 x 3 = 2 x 3⁴
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 3 = 2¹ x 3¹
Step 3: Multiply the common prime factors
2¹ x 3¹ = 2 x 3 = 6
The Greatest Common Factor of 12 and 162 is 6.
GCF of 12 and 162 Using Division Method or Euclidean Algorithm Method
Find the GCF of 12 and 162 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 162 by 12
162 ÷ 12 = 13 (quotient),
The remainder is calculated as 162 − (12×13) = 6
The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (12) by the previous remainder (6)
Divide 12 by 6
12 ÷ 6 = 2 (quotient),
remainder = 12 − (6×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 12 and 162 is 6.
Common Mistakes and How to Avoid Them in GCF of 12 and 162
Finding GCF of 12 and 162 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.X
For example, while listing factors of 12, 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 between 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 GCF of two numbers will always be an even number. But it's not true that 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 12 and 162 Examples
Problem 1
A chef has 12 apples and 162 oranges. She wants to make fruit baskets with the largest equal number of fruits in each basket. How many fruits will be in each basket?
We should find the GCF of 12 and 162
GCF of 12 and 162 2 x 3 = 6.
There are 6 equal baskets
12 ÷ 6 = 2
162 ÷ 6 = 27
There will be 6 baskets, and each basket gets 2 apples and 27 oranges.
Explanation
As the GCF of 12 and 162 is 6, the chef can make 6 baskets.
Now divide 12 and 162 by 6.
Each basket gets 2 apples and 27 oranges.
Problem 2
A library has 12 large books and 162 small books. They want to arrange them in shelves with the same number of books in each shelf, using the largest possible number of books per shelf. How many books will be in each shelf?
GCF of 12 and 162
2 x 3 = 6.
So each shelf will have 6 books.
Explanation
There are 12 large and 162 small books.
To find the total number of books in each shelf, we should find the GCF of 12 and 162.
There will be 6 books in each shelf.
Problem 3
A seamstress has 12 meters of silk fabric and 162 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 12 and 162
The GCF of 12 and 162 2 x 3 = 6.
The fabric pieces are 6 meters long.
Explanation
For calculating the longest length of the fabric pieces, first, we need to calculate the GCF of 12 and 162 which is 6.
The length of each piece of fabric will be 6 meters.
Problem 4
A carpenter has two wooden planks, one 12 cm long and the other 162 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 12 and 162 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, 12 cm and 162 cm, respectively.
We have to find the GCF of 12 and 162, which is 6 cm.
The longest length of each piece is 6 cm.
Problem 5
If the GCF of 12 and ‘a’ is 6, and the LCM is 324. Find ‘a’.
The value of ‘a’ is 162.
Explanation
GCF × LCM = product of the numbers
6 × 324 = 12 × a
1944 = 12a
a = 1944 ÷ 12 = 162
FAQs on the Greatest Common Factor of 12 and 162
1.What is the LCM of 12 and 162?
2.Is 12 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 162?
5.Are 12 and 162 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 12 and 162?
7.What are some fun ways kids in India can practice GCF of 12 and 162 with numbers?
8.What role do numbers and GCF of 12 and 162 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 12 and 162 skills?
Important Glossaries for GCF of 12 and 162
Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Prime Numbers: These are numbers greater than 1 that have no divisors other than 1 and themselves. For example, 2 and 3 are prime numbers.
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 162 are 2 and 3.
Remainder: The value left after division when the number cannot be divided evenly. For example, when 162 is divided by 12, the remainder is 6.
GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 12 and 162 is 6, as it is their largest common factor that divides the numbers completely.
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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.
