100 LearnersLast updated on July 30th, 2025
GCF of 42 and 63
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 42 and 63.
What is the GCF of 42 and 63?
The greatest common factor of 42 and 63 is 21. 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 are always positive.
How to find the GCF of 42 and 63?
To find the GCF of 42 and 63, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 42 and 63 by Using Listing of factors
Steps to find the GCF of 42 and 63 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42.
Factors of 63 = 1, 3, 7, 9, 21, 63.
Step 2: Now, identify the common factors of them. Common factors of 42 and 63: 1, 3, 7, 21.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 21.
The GCF of 42 and 63 is 21.
GCF of 42 and 63 Using Prime Factorization
To find the GCF of 42 and 63 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 63: 63 = 3 x 3 x 7
Step 2: Now, 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 63 is 21.
GCF of 42 and 63 Using Division Method or Euclidean Algorithm Method
Find the GCF of 42 and 63 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 63 by 42 63 ÷ 42 = 1 (quotient), The remainder is calculated as 63 − (42×1) = 21
The remainder is 21, not zero, so continue the process
Step 2: Now divide the previous divisor (42) by the previous remainder (21)
Divide 42 by 21 42 ÷ 21 = 2 (quotient), remainder = 42 − (21×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 42 and 63 is 21.
Common Mistakes and How to Avoid Them in GCF of 42 and 63
Finding the GCF of 42 and 63 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 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. However, it does not affect the GCF, but it indicates an 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; 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 63 Examples
Problem 1
A teacher has 42 books and 63 notebooks. 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 63 GCF of 42 and 63
3 x 7 = 21.
There are 21 equal groups
42 ÷ 21 = 2
63 ÷ 21 = 3
There will be 21 groups, and each group gets 2 books and 3 notebooks.
Explanation
As the GCF of 42 and 63 is 21, the teacher can make 21 groups.
Now divide 42 and 63 by 21.
Each group gets 2 books and 3 notebooks.
Problem 2
A school has 42 red chairs and 63 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 63 3 x 7 = 21. So each row will have 21 chairs.
Explanation
There are 42 red and 63 blue chairs. To find the total number of chairs in each row, we should find the GCF of 42 and 63. There will be 21 chairs in each row.
Problem 3
A tailor has 42 meters of red fabric and 63 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 42 and 63.
The GCF of 42 and 63
3 x 7 = 21.
The fabric is 21 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 42 and 63, which is 21. The length of each piece of fabric will be 21 meters.
Problem 4
A carpenter has two wooden planks, one 42 cm long and the other 63 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 63
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 63 cm, respectively, we have to find the GCF of 42 and 63, which is 21 cm. The longest length of each piece is 21 cm.
Problem 5
If the GCF of 42 and ‘a’ is 21, and the LCM is 126. Find ‘a’.
The value of ‘a’ is 63.
Explanation
GCF x LCM = product of the numbers
21 × 126 = 42 × a
2646 = 42a
a = 2646 ÷ 42 = 63
FAQs on the Greatest Common Factor of 42 and 63
1.What is the LCM of 42 and 63?
2.Is 42 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 63?
5.Are 42 and 63 prime numbers?
6.How can children in Vietnam use numbers in everyday life to understand GCF of 42 and 63?
7.What are some fun ways kids in Vietnam can practice GCF of 42 and 63 with numbers?
8.What role do numbers and GCF of 42 and 63 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve GCF of 42 and 63 skills?
Important Glossaries for GCF of 42 and 63
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 21 are 1, 3, 7, and 21.
- Prime Factorization: It involves expressing a number as the product of its prime numbers. For example, the prime factorization of 42 is 2 x 3 x 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 42 is divided by 5, the remainder is 2.
- LCM: The smallest common multiple of two or more numbers is termed the LCM. For example, the LCM of 42 and 63 is 126.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 42 and 63 is 21, as it is their largest common factor that divides the numbers completely.
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.
