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102 LearnersLast updated on September 24, 2025
GCF of 38 and 95
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 schedule events. In this topic, we will learn about the GCF of 38 and 95.
What is the GCF of 38 and 95?
The greatest common factor of 38 and 95 is 19. 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 38 and 95?
To find the GCF of 38 and 95, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 38 and 95 by Using Listing of factors
Steps to find the GCF of 38 and 95 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 38 = 1, 2, 19, 38. Factors of 95 = 1, 5, 19, 95.
Step 2: Now, identify the common factors of them Common factors of 38 and 95: 1, 19.
Step 3: Choose the largest factor The largest factor that both numbers have is 19. The GCF of 38 and 95 is 19.
GCF of 38 and 95 Using Prime Factorization
To find the GCF of 38 and 95 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 38: 38 = 2 × 19 Prime Factors of 95: 95 = 5 × 19
Step 2: Now, identify the common prime factors The common prime factor is: 19
Step 3: Multiply the common prime factors 19 = 19. The Greatest Common Factor of 38 and 95 is 19.
GCF of 38 and 95 Using Division Method or Euclidean Algorithm Method
Find the GCF of 38 and 95 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 95 by 38 95 ÷ 38 = 2 (quotient), The remainder is calculated as 95 − (38×2) = 19 The remainder is 19, not zero, so continue the process
Step 2: Now divide the previous divisor (38) by the previous remainder (19) Divide 38 by 19 38 ÷ 19 = 2 (quotient), remainder = 38 − (19×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 38 and 95 is 19.
Common Mistakes and How to Avoid Them in GCF of 38 and 95
Finding GCF of 38 and 95 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 38, students may mention 3 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 38 and 95 Examples
Problem 1
A farmer has 38 apple trees and 95 orange trees. He wants to plant them 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 38 and 95 GCF of 38 and 95 19. There are 19 equal groups 38 ÷ 19 = 2 95 ÷ 19 = 5 There will be 19 groups, and each group gets 2 apple trees and 5 orange trees.
Explanation
As the GCF of 38 and 95 is 19, the farmer can make 19 rows.
Now divide 38 and 95 by 19.
Each row gets 2 apple trees and 5 orange trees.
Problem 2
A library has 38 copies of one book and 95 copies of another. The librarian wants to arrange them on shelves with the same number of books on each shelf, using the largest possible number of books per shelf. How many books will be on each shelf?
GCF of 38 and 95 19. So each shelf will have 19 books.
Explanation
There are 38 copies of one book and 95 copies of another.
To find the total number of books on each shelf, we should find the GCF of 38 and 95.
There will be 19 books on each shelf.
Problem 3
A company has 38 meters of cable and 95 meters of wire. They want to cut both 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 38 and 95 The GCF of 38 and 95 19. The length of each piece is 19 meters.
Explanation
For calculating the longest length of the cable and wire first, we need to calculate the GCF of 38 and 95, which is 19.
The length of each piece will be 19 meters.
Problem 4
A decorator has two fabric rolls, one 38 meters long and the other 95 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 decorator needs the longest piece of fabric GCF of 38 and 95 19. The longest length of each piece is 19 meters.
Explanation
To find the longest length of each piece of the two fabric rolls, 38 meters and 95 meters, respectively.
We have to find the GCF of 38 and 95, which is 19 meters.
The longest length of each piece is 19 meters.
Problem 5
If the GCF of 38 and ‘b’ is 19, and the LCM is 190. Find ‘b’.
The value of ‘b’ is 95.
Explanation
GCF × LCM = product of the numbers
19 × 190 = 38 × b
3610 = 38b
b = 3610 ÷ 38
= 95
FAQs on the Greatest Common Factor of 38 and 95
1.What is the LCM of 38 and 95?
2.Is 38 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 95?
5.Are 38 and 95 prime numbers?
6.How can families in United States create number-rich environments to improve GCF of 38 and 95 skills?
7.What are some fun ways kids in United States can practice GCF of 38 and 95 with numbers?
8.What role do numbers and GCF of 38 and 95 play in helping children in United States develop problem-solving skills?
9.How can children in United States use numbers in everyday life to understand GCF of 38 and 95?
Important Glossaries for GCF of 38 and 95
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 38 are 1, 2, 19, and 38.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 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 95 are 5 and 19.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 95 is divided by 38, the remainder is 19.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 38 and 95 is 190.
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.
