104 LearnersLast updated on August 11th, 2025
GCF of 4 and 144
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 4 and 144.
What is the GCF of 4 and 144?
The greatest common factor of 4 and 144 is 4. 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 4 and 144?
To find the GCF of 4 and 144, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 4 and 144 by Using Listing of factors
Steps to find the GCF of 4 and 144 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 4 = 1, 2, 4. Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Step 2: Now, identify the common factors of them Common factors of 4 and 144: 1, 2, 4.
Step 3: Choose the largest factor The largest factor that both numbers have is 4.
The GCF of 4 and 144 is 4.
GCF of 4 and 144 Using Prime Factorization
To find the GCF of 4 and 144 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 4: 4 = 2 x 2 = 22 Prime Factors of 144: 144 = 2 x 2 x 2 x 2 x 3 x 3 = 24 x 32
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 = 22
Step 3: Multiply the common prime factors 22 = 4.
The Greatest Common Factor of 4 and 144 is 4.
GCF of 4 and 144 Using Division Method or Euclidean Algorithm Method
Find the GCF of 4 and 144 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 144 by 4 144 ÷ 4 = 36 (quotient),
The remainder is calculated as 144 − (4×36) = 0
The remainder is zero, so the divisor becomes the GCF.
The GCF of 4 and 144 is 4.
Common Mistakes and How to Avoid Them in GCF of 4 and 144
Finding the GCF of 4 and 144 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 4, 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. While it does not affect the GCF, it shows an incomplete understanding of 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; 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 4 and 144 Examples
Problem 1
A landscaper has 4 small flower pots and 144 large flower pots. He wants to arrange them into groups with the largest number of pots in each group. How many pots will be in each group?
We should find the GCF of 4 and 144. GCF of 4 and 144 is 4.
There are 4 equal groups. 4 ÷ 4 = 1 144 ÷ 4 = 36
There will be 4 groups, and each group gets 1 small pot and 36 large pots.
Explanation
As the GCF of 4 and 144 is 4, the landscaper can make 4 groups.
Now divide 4 and 144 by 4.
Each group gets 1 small pot and 36 large pots.
Problem 2
A school is organizing a sports event with 4 basketballs and 144 soccer balls. They want to make the largest possible groups with the same number of balls in each group. How many balls will be in each group?
GCF of 4 and 144 is 4. So each group will have 4 balls.
Explanation
There are 4 basketballs and 144 soccer balls.
To find the total number of balls in each group, we should find the GCF of 4 and 144.
There will be 4 balls in each group.
Problem 3
A chef has 4 liters of olive oil and 144 liters of vegetable oil. She wants to package them into containers of equal volume, using the largest possible volume. What should be the volume of each container?
For calculating the largest equal volume, we have to calculate the GCF of 4 and 144.
The GCF of 4 and 144 is 4.
The volume of each container is 4 liters.
Explanation
For calculating the largest volume of the containers, first, we need to calculate the GCF of 4 and 144, which is 4.
The volume of each container will be 4 liters.
Problem 4
A carpenter has two wooden beams, one 4 meters long and the other 144 meters 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 4 and 144 is 4.
The longest length of each piece is 4 meters.
Explanation
To find the longest length of each piece of the two wooden beams, 4 meters and 144 meters, respectively, we have to find the GCF of 4 and 144, which is 4 meters.
The longest length of each piece is 4 meters.
Problem 5
If the GCF of 4 and ‘a’ is 4, and the LCM is 144. Find ‘a’.
The value of ‘a’ is 144.
Explanation
GCF x LCM = product of the numbers 4 × 144 = 4 × a
576 = 4a
a = 576 ÷ 4 = 144
FAQs on the Greatest Common Factor of 4 and 144
1.What is the LCM of 4 and 144?
2.Is 4 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 144?
5.Are 4 and 144 prime numbers?
6.How can children in United Kingdom use numbers in everyday life to understand GCF of 4 and 144?
7.What are some fun ways kids in United Kingdom can practice GCF of 4 and 144 with numbers?
8.What role do numbers and GCF of 4 and 144 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve GCF of 4 and 144 skills?
Important Glossaries for GCF of 4 and 144
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 4 are 1, 2, and 4.
- 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 144 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 5, the remainder is 2, and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed the LCM. For example, the LCM of 4 and 144 is 144.
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.
