100 LearnersLast updated on August 13th, 2025
GCF of 75 and 48
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 75 and 48.
What is the GCF of 75 and 48?
The greatest common factor of 75 and 48 is 3. 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, which are always positive.
How to find the GCF of 75 and 48?
To find the GCF of 75 and 48, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 75 and 48 by Using Listing of factors
Steps to find the GCF of 75 and 48 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 75 = 1, 3, 5, 15, 25, 75.
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Step 2: Now, identify the common factors of them Common factors of 75 and 48: 1, 3.
Step 3: Choose the largest factor The largest factor that both numbers have is 3. The GCF of 75 and 48 is 3.
GCF of 75 and 48 Using Prime Factorization
To find the GCF of 75 and 48 using Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number
Prime Factors of 75: 75 = 3 x 5 x 5 = 3 x 5²
Prime Factors of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3
Step 2: Now, identify the common prime factors The common prime factors are: 3
Step 3: Multiply the common prime factors 3 The Greatest Common Factor of 75 and 48 is 3.
GCF of 75 and 48 Using Division Method or Euclidean Algorithm Method
Find the GCF of 75 and 48 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 75 by 48 75 ÷ 48 = 1 (quotient) The remainder is calculated as 75 − (48×1) = 27 The remainder is 27, not zero, so continue the process
Step 2: Now divide the previous divisor (48) by the previous remainder (27) Divide 48 by 27 48 ÷ 27 = 1 (quotient), remainder = 48 − (27×1) = 21 The remainder is 21, not zero, so continue the process
Step 3: Now divide the previous divisor (27) by the previous remainder (21) Divide 27 by 21 27 ÷ 21 = 1 (quotient), remainder = 27 − (21×1) = 6 The remainder is 6, not zero, so continue the process
Step 4: Now divide the previous divisor (21) by the previous remainder (6) Divide 21 by 6 21 ÷ 6 = 3 (quotient), remainder = 21 − (6×3) = 3 The remainder is 3, not zero, so continue the process
Step 5: Now divide the previous divisor (6) by the previous remainder (3) Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 − (3×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 75 and 48 is 3.
Common Mistakes and How to Avoid Them in GCF of 75 and 48
Finding GCF of 75 and 48 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 75, 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 75 and 48 Examples
Problem 1
A gardener has 75 roses and 48 tulips. She wants to plant them in rows with the largest number of flowers in each row. How many flowers will be in each row?
We should find GCF of 75 and 48 GCF of 75 and 48 3
There are 3 equal groups 75 ÷ 3 = 25 48 ÷ 3 = 16
There will be 3 groups, and each group gets 25 roses and 16 tulips.
Explanation
As the GCF of 75 and 48 is 3, the gardener can make 3 groups. Now divide 75 and 48 by 3. Each group gets 25 roses and 16 tulips.
Problem 2
A chef has 75 apples and 48 oranges. He wants to create fruit baskets with the largest possible number of fruits in each basket. How many fruits will be in each basket?
GCF of 75 and 48 3 So each basket will have 3 fruits.
Explanation
There are 75 apples and 48 oranges. To find the total number of fruits in each basket, we should find the GCF of 75 and 48. There will be 3 fruits in each basket.
Problem 3
A tailor has 75 meters of fabric A and 48 meters of fabric B. He 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 longest equal length, we have to calculate the GCF of 75 and 48 The GCF of 75 and 48 3 The fabric is 3 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 75 and 48 which is 3. The length of each piece of the fabric will be 3 meters.
Problem 4
A carpenter has two wooden planks, one 75 cm long and the other 48 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 75 and 48 3 The longest length of each piece is 3 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 75 cm and 48 cm, respectively. We have to find the GCF of 75 and 48, which is 3 cm. The longest length of each piece is 3 cm.
Problem 5
If the GCF of 75 and ‘b’ is 15, and the LCM is 300. Find ‘b’.
The value of ‘b’ is 60.
Explanation
GCF x LCM = product of the numbers
15 × 300 = 75 × b
4500 = 75b
b = 4500 ÷ 75 = 60
FAQs on the Greatest Common Factor of 75 and 48
1.What is the LCM of 75 and 48?
2.Is 75 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 48?
5.Are 75 and 48 prime numbers?
6.How can children in Indonesia use numbers in everyday life to understand GCF of 75 and 48?
7.What are some fun ways kids in Indonesia can practice GCF of 75 and 48 with numbers?
8.What role do numbers and GCF of 75 and 48 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve GCF of 75 and 48 skills?
Important Glossaries for GCF of 75 and 48
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.
- 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 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 4, the remainder is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 75 and 48 is 1200.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 75 and 48 will be 3, 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.
