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103 LearnersLast updated on September 18, 2025
GCF of 42 and 21
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 42 and 21.
What is the GCF of 42 and 21?
The greatest common factor of 42 and 21 is 21. 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 42 and 21?
To find the GCF of 42 and 21, several methods can be used, including
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 42 and 21 by Listing Factors
Steps to find the GCF of 42 and 21 using the listing of factors:
Step 1: List the factors of each number
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42.
Factors of 21 = 1, 3, 7, 21.
Step 2: Identify the common factors Common factors of 42 and 21: 1, 3, 7, 21.
Step 3: Choose the largest factor The largest factor that both numbers have is 21. The GCF of 42 and 21 is 21.
GCF of 42 and 21 Using Prime Factorization
To find the GCF of 42 and 21 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 42: 42 = 2 x 3 x 7
Prime Factors of 21: 21 = 3 x 7
Step 2: Identify the common prime factors The common prime factors are: 3 x 7
Step 3: Multiply the common prime factors 3 x 7 = 21. The Greatest Common Factor of 42 and 21 is 21.
GCF of 42 and 21 Using Division Method or Euclidean Algorithm
Find the GCF of 42 and 21 using the division method or Euclidean Algorithm. Follow these steps:
Step 1: Divide the larger number by the smaller number Here, divide 42 by 21 42 ÷ 21 = 2 (quotient), remainder = 42 - (21 x 2) = 0
The remainder is zero, so the divisor is the GCF.
The GCF of 42 and 21 is 21.
Common Mistakes and How to Avoid Them in GCF of 42 and 21
Finding the GCF of 42 and 21 seems simple, but students often make mistakes while calculating it. Here are some common mistakes to avoid.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 42, 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. Although it does not affect the GCF, it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students often confuse factors and multiples. In that confusion, they may write multiples instead of factors. To avoid this, 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; 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 42 and 21 Examples
Problem 1
A teacher has 42 notebooks and 21 markers. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 42 and 21 GCF of 42 and 21 3 x 7 = 21.
There are 21 equal groups 42 ÷ 21 = 2 21 ÷ 21 = 1
There will be 21 groups, and each group gets 2 notebooks and 1 marker.
Explanation
As the GCF of 42 and 21 is 21, the teacher can make 21 groups.
Now divide 42 and 21 by 21.
Each group gets 2 notebooks and 1 marker.
Problem 2
A school has 42 red chairs and 21 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 42 and 21 3 x 7 = 21. So each row will have 21 chairs.
Explanation
There are 42 red and 21 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 42 and 21.
There will be 21 chairs in each row.
Problem 3
A tailor has 42 meters of red ribbon and 21 meters of blue ribbon. She wants to cut both ribbons 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 42 and 21
The GCF of 42 and 21 3 x 7 = 21.
The length of each piece is 21 meters.
Explanation
To calculate the longest length of the ribbon, first, we need to calculate the GCF of 42 and 21, which is 21.
The length of each piece of the ribbon will be 21 meters.
Problem 4
A carpenter has two wooden planks, one 42 cm long and the other 21 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 42 and 21 3 x 7 = 21.
The longest length of each piece is 21 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 42 cm and 21 cm, respectively, we have to find the GCF of 42 and 21, which is 21 cm.
The longest length of each piece is 21 cm.
Problem 5
If the GCF of 42 and ‘b’ is 21, and the LCM is 84, find ‘b’.
The value of ‘b’ is 42.
Explanation
GCF x LCM = product of the numbers
21 x 84 = 42 x b
1764 = 42b
b = 1764 ÷ 42 = 42
FAQs on the Greatest Common Factor of 42 and 21
1.What is the LCM of 42 and 21?
2.Is 42 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 21?
5.Are 42 and 21 prime numbers?
Important Glossaries for GCF of 42 and 21
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 21 are 1, 3, 7, and 21.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, 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 21 are 3 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 43 is divided by 21, the remainder is 1 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 42 and 21 is 42.
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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.
