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106 LearnersLast updated on September 23, 2025
GCF of 5 and 24
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 to schedule events. In this topic, we will learn about the GCF of 5 and 24.
What is the GCF of 5 and 24?
The greatest common factor of 5 and 24 is 1. 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 5 and 24?
To find the GCF of 5 and 24, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 5 and 24 by Using Listing of factors
Steps to find the GCF of 5 and 24 using the listing of factors: Step 1: Firstly, list the factors of each number Factors of 5 = 1, 5. Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24. Step 2: Now, identify the common factors of them Common factor of 5 and 24: 1. Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 5 and 24 is 1.
GCF of 5 and 24 Using Prime Factorization
To find the GCF of 5 and 24 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 5: 5 = 5
Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 2³ x 3
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Multiply the common prime factors Since there are no common prime factors, the GCF is 1. The Greatest Common Factor of 5 and 24 is 1.
GCF of 5 and 24 Using Division Method or Euclidean Algorithm Method
Find the GCF of 5 and 24 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 24 by 5 24 ÷ 5 = 4 (quotient), The remainder is calculated as 24 − (5×4) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (5) by the previous remainder (4) Divide 5 by 4 5 ÷ 4 = 1 (quotient), remainder = 5 − (4×1) = 1
Step 3: Continue dividing Now divide the previous divisor (4) by the previous remainder (1) 4 ÷ 1 = 4 (quotient), remainder = 0
The remainder is zero, so the divisor will become the GCF. The GCF of 5 and 24 is 1.
Common Mistakes and How to Avoid Them in GCF of 5 and 24
Finding the GCF of 5 and 24 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 24, 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 a factor other than 1 for co-prime numbers. 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. For co-prime numbers, 1 is the only common factor. 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 a number greater than 1
Students may assume that the GCF of two numbers will always be more than 1. But it's not true for co-prime numbers, as their GCF is 1. To avoid this, students should focus on common factors and not just assume a number greater than 1.
Greatest Common Factor of 5 and 24 Examples
Problem 1
A baker has 5 loaves of bread and 24 cupcakes. She wants to pack them into equal sets with the largest number of items in each set. How many items will be in each set?
We should find the GCF of 5 and 24. The GCF of 5 and 24 is 1.
There are 1 equal group. 5 ÷ 1 = 5 24 ÷ 1 = 24
There will be 1 group with 5 loaves of bread and 24 cupcakes.
Explanation
As the GCF of 5 and 24 is 1, the baker can make 1 group. The entire set consists of 5 loaves of bread and 24 cupcakes.
Problem 2
A gardener has 5 rose bushes and 24 tulip plants. They want to arrange them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
The GCF of 5 and 24 is 1. So each row will have 1 plant.
Explanation
There are 5 rose bushes and 24 tulip plants. To find the total number of plants in each row, we should find the GCF of 5 and 24. There will be 1 plant in each row.
Problem 3
A painter has a 5-meter long canvas and a 24-meter long canvas. She wants to cut both canvases 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 5 and 24.
The GCF of 5 and 24 is 1.
The piece is 1 meter long.
Explanation
For calculating the longest length of the canvas pieces, we first need to calculate the GCF of 5 and 24, which is 1. The length of each piece of the canvas will be 1 meter.
Problem 4
A tailor has two fabrics, one 5 meters long and the other 24 meters long. She wants to cut them into equal pieces with the longest possible length and no fabric left over. What should be the length of each piece?
The tailor needs the longest piece of fabric.
The GCF of 5 and 24 is 1.
The longest length of each piece is 1 meter.
Explanation
To find the longest length of each piece of the two fabrics, 5 meters and 24 meters respectively, we have to find the GCF of 5 and 24, which is 1 meter. The longest length of each piece is 1 meter.
Problem 5
If the GCF of 5 and ‘b’ is 1, and the LCM is 120. Find ‘b’.
The value of ‘b’ is 24.
Explanation
GCF x LCM = product of the numbers
1 × 120 = 5 × b
120 = 5b
b = 120 ÷ 5 = 24
FAQs on the Greatest Common Factor of 5 and 24
1.What is the LCM of 5 and 24?
2.Is 5 a factor of 24?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 24?
5.Are 5 and 24 prime numbers?
Important Glossaries for GCF of 5 and 24
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 5 are 1 and 5.
- 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 factor of 5 is 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 5 is divided by 2, the remainder is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 24 is 120.
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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.
