104 LearnersLast updated on August 5th, 2025
GCF of 42 and 84
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 42 and 84.
What is the GCF of 42 and 84?
The greatest common factor of 42 and 84 is 42. 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 84?
To find the GCF of 42 and 84, a few methods are described below: -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 42 and 84 by Using Listing of Factors
Steps to find the GCF of 42 and 84 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 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Step 2: Now, identify the common factors of them Common factors of 42 and 84: 1, 2, 3, 6, 7, 14, 21, 42.
Step 3: Choose the largest factor
The largest factor that both numbers have is 42.
The GCF of 42 and 84 is 42.
GCF of 42 and 84 Using Prime Factorization
To find the GCF of 42 and 84 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 84: 84 = 2 x 2 x 3 x 7
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 3 x 7
Step 3: Multiply the common prime factors 2 x 3 x 7 = 42.
The Greatest Common Factor of 42 and 84 is 42.
GCF of 42 and 84 Using Division Method or Euclidean Algorithm Method
Find the GCF of 42 and 84 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 84 by 42 84 ÷ 42 = 2 (quotient),
The remainder is calculated as 84 − (42×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 42 and 84 is 42.
Common Mistakes and How to Avoid Them in GCF of 42 and 84
Finding GCF of 42 and 84 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 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 42 and 84 Examples
Problem 1
A gardener has 42 apple trees and 84 orange trees. They want to plant the trees in rows, with the largest possible number of trees in each row. How many trees will be in each row?
We should find the GCF of 42 and 84 GCF of 42 and 84 is 42.
There are 42 equal groups. 42 ÷ 42 = 1 84 ÷ 42 = 2
There will be 42 groups, and each group has 1 apple tree and 2 orange trees.
Explanation
As the GCF of 42 and 84 is 42, the gardener can make 42 groups. Now divide 42 and 84 by 42. Each group has 1 apple tree and 2 orange trees.
Problem 2
A school has 42 red chairs and 84 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 84 is 42.
So each row will have 42 chairs.
Explanation
There are 42 red and 84 blue chairs. To find the total number of chairs in each row, we should find the GCF of 42 and 84. There will be 42 chairs in each row.
Problem 3
A chef has 42 meters of red ribbon and 84 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 84
The GCF of 42 and 84 is 42.
The ribbon is 42 meters long.
Explanation
For calculating the longest length of the ribbon first we need to calculate the GCF of 42 and 84 which is 42. The length of each piece of the ribbon will be 42 meters.
Problem 4
A carpenter has two wooden planks, one 42 cm long and the other 84 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 84 is 42.
The longest length of each piece is 42 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 42 cm and 84 cm, respectively. We have to find the GCF of 42 and 84, which is 42 cm. The longest length of each piece is 42 cm.
Problem 5
If the GCF of 42 and ‘a’ is 42, and the LCM is 168, find ‘a’.
The value of ‘a’ is 84.
Explanation
GCF x LCM = product of the numbers 42 × 168 = 42 × a
7056 = 42a
a = 7056 ÷ 42 = 84
FAQs on the Greatest Common Factor of 42 and 84
1.What is the LCM of 42 and 84?
2.Is 42 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 84?
5.Are 42 and 84 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 42 and 84?
7.What are some fun ways kids in United States can practice GCF of 42 and 84 with numbers?
8.What role do numbers and GCF of 42 and 84 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 42 and 84 skills?
Important Glossaries for GCF of 42 and 84
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
- 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 42 are 2, 3, and 7.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 42 and 84 is 42, as it is their largest common factor that divides the numbers completely.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 84 is divided by 42, the remainder is 0.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 42 and 84 is 84.
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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.
