100 LearnersLast updated on August 5th, 2025
GCF of 12 and 35
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 35.
What is the GCF of 12 and 35?
The greatest common factor of 12 and 35 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 35?
To find the GCF of 12 and 35, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 12 and 35 by Using Listing of Factors
Steps to find the GCF of 12 and 35 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 35 = 1, 5, 7, 35.
Step 2: Now, identify the common factors of them Common factor of 12 and 35: 1.
Step 3: Choose the largest factor
The largest factor that both numbers have is 1.
The GCF of 12 and 35 is 1.
GCF of 12 and 35 Using Prime Factorization
To find the GCF of 12 and 35 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 35: 35 = 5 x 7
Step 2: Now, identify the common prime factors
There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 12 and 35 is 1.
GCF of 12 and 35 Using Division Method or Euclidean Algorithm Method
Find the GCF of 12 and 35 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 35 by 12 35 ÷ 12 = 2 (quotient),
The remainder is calculated as 35 − (12×2) = 11
The remainder is 11, not zero, so continue the process
Step 2: Now divide the previous divisor (12) by the previous remainder (11)
Divide 12 by 11 12 ÷ 11 = 1 (quotient), remainder = 12 − (11×1) = 1
The remainder is 1, not zero, so continue the process
Step 3: Now divide the previous divisor (11) by the previous remainder (1)
Divide 11 by 1 11 ÷ 1 = 11 (quotient), remainder = 11 − (1×11) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 12 and 35 is 1.
Common Mistakes and How to Avoid Them in GCF of 12 and 35
Finding the GCF of 12 and 35 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 10, 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 the 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 35 Examples
Problem 1
A gardener has 12 roses and 35 tulips. She wants to group them into sets with the largest number of flowers in each group without mixing roses and tulips. How many flowers will be in each group?
We should find the GCF of 12 and 35 GCF of 12 and 35 is 1.
There will be 1 flower in each group.
Explanation
As the GCF of 12 and 35 is 1, the gardener can only make groups with 1 flower each, so each group will have either a rose or a tulip but not both.
Problem 2
A library has 12 fiction books and 35 nonfiction books. They want to arrange them in stacks with the same number of books in each stack, using the largest possible number of books per stack. How many books will be in each stack?
GCF of 12 and 35 is 1.
So each stack will have 1 book.
Explanation
There are 12 fiction and 35 nonfiction books.
To find the total number of books in each stack, we should find the GCF of 12 and 35.
There will be 1 book in each stack.
Problem 3
A chef has 12 apples and 35 bananas. She wants to create fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?
For calculating the largest equal number of fruits, we have to calculate the GCF of 12 and 35 The GCF of 12 and 35 is 1. Each basket will have 1 fruit.
Explanation
For calculating the largest number of fruits in each basket, first, we need to calculate the GCF of 12 and 35, which is 1.
Each basket will have 1 fruit.
Problem 4
A painter has two rolls of canvas, one 12 meters long and the other 35 meters long. He wants to cut them into the longest possible equal pieces, without any canvas left over. What should be the length of each piece?
The painter needs the longest piece of canvas GCF of 12 and 35 is 1.
The longest length of each piece is 1 meter.
Explanation
To find the longest length of each piece of the two canvas rolls, 12 meters and 35 meters, respectively, we have to find the GCF of 12 and 35, which is 1 meter. The longest length of each piece is 1 meter.
Problem 5
If the GCF of 12 and ‘b’ is 1, and the LCM is 420, find ‘b’.
The value of ‘b’ is 35.
Explanation
GCF x LCM = product of the numbers 1 × 420 = 12 × b
420 = 12b
b = 420 ÷ 12 = 35
FAQs on the Greatest Common Factor of 12 and 35
1.What is the LCM of 12 and 35?
2.Is 12 divisible by 3?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 12?
5.Are 12 and 35 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 12 and 35?
7.What are some fun ways kids in United States can practice GCF of 12 and 35 with numbers?
8.What role do numbers and GCF of 12 and 35 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 12 and 35 skills?
Important Glossaries for GCF of 12 and 35
- 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 greater than 1 that have no divisors other than 1 and the number itself. For example, 5 and 7 are prime numbers.
- Co-prime Numbers: Two or more numbers that have no common factors other than 1. For example, 8 and 15 are co-prime.
- Prime Factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 x 3².
- LCM: The smallest common multiple of two or more numbers. For example, the LCM of 12 and 35 is 420.
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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.
