Summarize this article:
104 LearnersLast updated on September 24, 2025
GCF of 42 and 154
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 to schedule events. In this topic, we will learn about the GCF of 42 and 154.
What is the GCF of 42 and 154?
The greatest common factor of 42 and 154 is 14. 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 154?
To find the GCF of 42 and 154, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 42 and 154 by Using Listing of Factors
Steps to find the GCF of 42 and 154 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 154 = 1, 2, 7, 11, 14, 22, 77, 154.
Step 2: Now, identify the common factors of them Common factors of 42 and 154: 1, 2, 7, 14.
Step 3: Choose the largest factor The largest factor that both numbers have is 14. The GCF of 42 and 154 is 14.
GCF of 42 and 154 Using Prime Factorization
To find the GCF of 42 and 154 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 154: 154 = 2 x 7 x 11
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 7
Step 3: Multiply the common prime factors 2 x 7 = 14.
The Greatest Common Factor of 42 and 154 is 14.
GCF of 42 and 154 Using Division Method or Euclidean Algorithm Method
Find the GCF of 42 and 154 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 154 by 42 154 ÷ 42 = 3 (quotient), The remainder is calculated as 154 − (42×3) = 28 The remainder is 28, not zero, so continue the process
Step 2: Now divide the previous divisor (42) by the previous remainder (28) Divide 42 by 28 42 ÷ 28 = 1 (quotient), remainder = 42 − (28×1) = 14
Step 3: Divide 28 by the remainder 14 28 ÷ 14 = 2 (quotient), remainder = 28 − (14×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 42 and 154 is 14.
Common Mistakes and How to Avoid Them in GCF of 42 and 154
Finding GCF of 42 and 154 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 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 154 Examples
Problem 1
A farmer has 42 apple trees and 154 orange trees. He wants to plant them in equal rows, with the largest number of trees in each row. How many trees will be in each row?
We should find the GCF of 42 and 154 GCF of 42 and 154 2 x 7 = 14. There will be 14 equal rows 42 ÷ 14 = 3 154 ÷ 14 = 11 There will be 14 rows, and each row gets 3 apple trees and 11 orange trees.
Explanation
As the GCF of 42 and 154 is 14, the farmer can make 14 rows.
Now divide 42 and 154 by 14.
Each row gets 3 apple trees and 11 orange trees.
Problem 2
A gardener has 42 rose bushes and 154 tulip bulbs. They want to arrange them in clusters with the same number of plants in each cluster, using the largest possible number of plants per cluster. How many plants will be in each cluster?
GCF of 42 and 154 2 x 7 = 14. So each cluster will have 14 plants.
Explanation
There are 42 rose bushes and 154 tulip bulbs.
To find the total number of plants in each cluster, we should find the GCF of 42 and 154.
There will be 14 plants in each cluster.
Problem 3
A seamstress has 42 meters of silk and 154 meters of cotton. 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 154 The GCF of 42 and 154 2 x 7 = 14. The fabric is 14 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 42 and 154 which is 14.
The length of each piece of the fabric will be 14 meters.
Problem 4
A carpenter has two wooden planks, one 42 cm long and the other 154 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 154 2 x 7 = 14. The longest length of each piece is 14 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 42 cm and 154 cm, respectively.
We have to find the GCF of 42 and 154, which is 14 cm.
The longest length of each piece is 14 cm.
Problem 5
If the GCF of 42 and ‘b’ is 14, and the LCM is 462. Find ‘b’.
The value of ‘b’ is 154.
Explanation
GCF x LCM = product of the numbers
14 x 462 = 42 x b
6468 = 42b
b = 6468 ÷ 42
= 154
FAQs on the Greatest Common Factor of 42 and 154
1.What is the LCM of 42 and 154?
2.Is 42 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 154?
5.Are 42 and 154 prime numbers?
Important Glossaries for GCF of 42 and 154
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 14 are 1, 2, 7, and 14.
- 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.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 20 is divided by 6, the remainder is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 42 and 154 is 462.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 42 and 154 is 14, as it is their largest common factor that divides the numbers completely.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 42 and 154
![Important Math Links Icon]()
Next to GCF of 42 and 154
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.
