101 LearnersLast updated on August 5th, 2025
GCF of 42 and 96
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 96.
What is the GCF of 42 and 96?
The greatest common factor of 42 and 96 is 6. 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 96?
To find the GCF of 42 and 96, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 42 and 96 by Using Listing of factors
Steps to find the GCF of 42 and 96 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 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.
Step 2: Now, identify the common factors of them
Common factors of 42 and 96: 1, 2, 3, 6.
Step 3: Choose the largest factor
The largest factor that both numbers have is 6.
The GCF of 42 and 96 is 6.
GCF of 42 and 96 Using Prime Factorization
To find the GCF of 42 and 96 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 96: 96 = 2 x 2 x 2 x 2 x 2 x 3 = 25 x 3
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 3
Step 3: Multiply the common prime factors 2 x 3 = 6.
The Greatest Common Factor of 42 and 96 is 6.
GCF of 42 and 96 Using Division Method or Euclidean Algorithm Method
Find the GCF of 42 and 96 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 96 by 42 96 ÷ 42 = 2 (quotient),
The remainder is calculated as 96 − (42×2) = 12
The remainder is 12, not zero, so continue the process
Step 2: Now divide the previous divisor (42) by the previous remainder (12)
Divide 42 by 12 42 ÷ 12 = 3 (quotient), remainder = 42 − (12×3) = 6
The remainder is not zero, so continue the process
Step 3: Divide the previous divisor (12) by the previous remainder (6) 12 ÷ 6 = 2 (quotient), remainder = 12 − (6×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 42 and 96 is 6.
Common Mistakes and How to Avoid Them in GCF of 42 and 96
Finding GCF of 42 and 96 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 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 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 96 Examples
Problem 1
A gardener has 42 rose bushes and 96 tulip bulbs. He wants to divide them into the largest equal groups possible. How many plants will be in each group?
We should find GCF of 42 and 96 The GCF of 42 and 96 is 6. 42 ÷ 6 = 7 96 ÷ 6 = 16 There will be 6 groups, and each group will contain 7 rose bushes and 16 tulip bulbs.
Explanation
As the GCF of 42 and 96 is 6, the gardener can make 6 groups.
Now divide 42 and 96 by 6.
Each group will have 7 rose bushes and 16 tulip bulbs.
Problem 2
A mechanic has 42 wrenches and 96 screwdrivers. He wants to organize them into toolkits with the greatest number of each tool in every kit. How many tools will each toolkit have?
The GCF of 42 and 96 is 6. So each toolkit will have 6 tools.
Explanation
There are 42 wrenches and 96 screwdrivers.
To find the total number of tools in each toolkit, we should find the GCF of 42 and 96.
There will be 6 tools in each toolkit.
Problem 3
A chef has 42 kg of potatoes and 96 kg of onions. She wants to pack them into bags with the largest possible weight each. What should be the weight of each bag?
For calculating the largest equal weight, we have to calculate the GCF of 42 and 96. The GCF of 42 and 96 is 6. Each bag will weigh 6 kg.
Explanation
For calculating the largest weight of the bags, first we need to calculate the GCF of 42 and 96, which is 6.
The weight of each bag will be 6 kg.
Problem 4
A tailor has two bolts of fabric, one 42 meters long and the other 96 meters long. She wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?
The tailor needs the longest piece of fabric. The GCF of 42 and 96 is 6. The longest length of each piece is 6 meters.
Explanation
To find the longest length of each piece of the two bolts of fabric, 42 meters and 96 meters, respectively.
have to find the GCF of 42 and 96, which is 6 meters.
The longest length of each piece is 6 meters.
Problem 5
If the GCF of 42 and ‘b’ is 6, and the LCM is 672. Find ‘b’.
The value of ‘b’ is 96.
Explanation
GCF x LCM = product of the numbers
6 × 672 = 42 × b
4032 = 42b
b = 4032 ÷ 42 = 96
FAQs on the Greatest Common Factor of 42 and 96
1.What is the LCM of 42 and 96?
2.Is 42 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 96?
5.Are 42 and 96 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 42 and 96?
7.What are some fun ways kids in India can practice GCF of 42 and 96 with numbers?
8.What role do numbers and GCF of 42 and 96 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 42 and 96 skills?
Important Glossaries for GCF of 42 and 96
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, 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 15 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 42 and 96 is 672.
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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.
