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101 LearnersLast updated on September 9, 2025
GCF of 12 and 13
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 12 and 13.
What is the GCF of 12 and 13?
The greatest common factor of 12 and 13 is 1. 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 12 and 13?
To find the GCF of 12 and 13, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 12 and 13 by Using Listing of Factors
Steps to find the GCF of 12 and 13 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 13 = 1, 13.
Step 2: Now, identify the common factors of them Common factor of 12 and 13: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 12 and 13 is 1.
GCF of 12 and 13 Using Prime Factorization
To find the GCF of 12 and 13 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 13: 13 = 13 (since 13 is a prime number)
Step 2: Identify the common prime factors There are no common prime factors.
Step 3: If no common prime factors exist, the GCF is 1. The Greatest Common Factor of 12 and 13 is 1.
GCF of 12 and 13 Using Division Method or Euclidean Algorithm Method
Find the GCF of 12 and 13 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 13 by 12 13 ÷ 12 = 1 (quotient),
The remainder is calculated as 13 − (12 x 1) = 1
The remainder is 1, not zero, so continue the process
Step 2: Now divide the previous divisor (12) by the previous remainder (1)
Divide 12 by 1 12 ÷ 1 = 12 (quotient), remainder = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 12 and 13 is 1.
Common Mistakes and How to Avoid Them in GCF of 12 and 13
Finding the GCF of 12 and 13 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 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 a wrong common factor, thinking there is one when there is not.
To avoid this confusion, students should list all the common factors (if any) and find the greatest one, which in this case is 1.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers.
However, it is crucial for understanding that 1 is the only common factor when numbers are co-prime. Students should always include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students may 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 greater than 1
Students may assume that the GCF of two numbers is always greater than 1. But for co-prime numbers, the GCF is 1.
Students should focus on common factors rather than assumptions about numerical value.
Greatest Common Factor of 12 and 13 Examples
Problem 1
A teacher has 12 apples and 13 oranges. She wants to group them into sets with the same number of fruits in each set, using the largest number possible. How many fruits will be in each set?
We should find the GCF of 12 and 13 GCF of 12 and 13 is 1. There will be 1 fruit in each set.
Explanation
As the GCF of 12 and 13 is 1, the teacher can only make sets of 1 fruit.
Each set will have 1 fruit because 12 and 13 have no common factors other than 1.
Problem 2
A garden has 12 red flowers and 13 blue flowers. They want to plant them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?
GCF of 12 and 13 is 1. So each row will have 1 flower.
Explanation
There are 12 red and 13 blue flowers.
To find the total number of flowers in each row, we should find the GCF of 12 and 13.
There will be 1 flower in each row.
Problem 3
A tailor has 12 meters of red fabric and 13 meters of blue 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 13
The GCF of 12 and 13 is 1.
The fabric pieces will be 1 meter long.
Explanation
To calculate the longest length of the fabric, first, we need to calculate the GCF of 12 and 13, which is 1.
The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 12 cm long and the other 13 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 13 is 1. The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 12 cm and 13 cm, respectively, we have to find the GCF of 12 and 13, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 12 and ‘b’ is 1, and the LCM is 12 x b. Find ‘b’.
The value of ‘b’ is 13.
Explanation
GCF x LCM = product of the numbers 1 x (12 x b) = 12 x b
Since the GCF is 1, 'b' must be a number that is co-prime with 12, such as 13.
FAQs on the Greatest Common Factor of 12 and 13
1.What is the LCM of 12 and 13?
2.Is 12 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 13?
5.Are 12 and 13 prime numbers?
Important Glossaries for GCF of 12 and 13
- 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: Numbers that have only two factors, 1 and the number itself. For example, 13 is a prime number.
- Co-prime Numbers: Two numbers that have no common factors other than 1. For example, 12 and 13 are co-prime.
- Euclidean Algorithm: A method to find the GCF of two numbers by using division and remainders.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 12 and 13 is 1, as it is their largest common factor.
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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.
