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102 LearnersLast updated on September 12, 2025
GCF of 15 and 24
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 15 and 24.
What is the GCF of 15 and 24?
The greatest common factor of 15 and 24 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 are always positive.
How to find the GCF of 15 and 24?
To find the GCF of 15 and 24, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 15 and 24 by Using Listing of Factors
Steps to find the GCF of 15 and 24 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 15 = 1, 3, 5, 15. Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Step 2: Now, identify the common factors of them Common factors of 15 and 24: 1, 3.
Step 3: Choose the largest factor The largest factor that both numbers have is 3. The GCF of 15 and 24 is 3.
GCF of 15 and 24 Using Prime Factorization
To find the GCF of 15 and 24 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime factors of 15: 15 = 3 × 5
Prime factors of 24: 24 = 2 × 2 × 2 × 3 = 2³ × 3
Step 2: Now, identify the common prime factors The common prime factor is: 3
Step 3: Multiply the common prime factors 3 = 3 The Greatest Common Factor of 15 and 24 is 3.
GCF of 15 and 24 Using Division Method or Euclidean Algorithm Method
Find the GCF of 15 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 15 24 ÷ 15 = 1 (quotient) The remainder is calculated as 24 − (15×1) = 9 The remainder is 9, not zero, so continue the process
Step 2: Now divide the previous divisor (15) by the previous remainder (9) Divide 15 by 9 15 ÷ 9 = 1 (quotient), remainder = 15 − (9×1) = 6
Step 3: Continue the process Now divide the previous divisor (9) by the previous remainder (6) Divide 9 by 6 9 ÷ 6 = 1 (quotient), remainder = 9 − (6×1) = 3
Step 4: Continue the process 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 15 and 24 is 3.
Common Mistakes and How to Avoid Them in GCF of 15 and 24
Finding GCF of 15 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 15, 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 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 15 and 24 Examples
Problem 1
A baker has 15 loaves of whole wheat bread and 24 loaves of rye bread. He wants to pack them in boxes with the largest number of loaves per box, equally. How many loaves will be in each box?
We should find the GCF of 15 and 24 GCF of 15 and 24 = 3
There are 3 equal groups 15 ÷ 3 = 5
24 ÷ 3 = 8
There will be 3 groups, and each box gets 5 loaves of whole wheat bread and 8 loaves of rye bread.
Explanation
As the GCF of 15 and 24 is 3, the baker can make 3 groups. Now divide 15 and 24 by 3. Each box gets 5 loaves of whole wheat bread and 8 loaves of rye bread.
Problem 2
A gardener has 15 pots of red roses and 24 pots of white roses. She wants to arrange them in rows with the same number of pots in each row, using the largest possible number of pots per row. How many pots will be in each row?
GCF of 15 and 24 3 = 3
So each row will have 3 pots.
Explanation
There are 15 pots of red roses and 24 pots of white roses. To find the total number of pots in each row, we should find the GCF of 15 and 24. There will be 3 pots in each row.
Problem 3
A chef has 15 meters of sausage casing and 24 meters of vegetable wrap. She wants 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 15 and 24 The GCF of 15 and 24 = 3 The length of each piece is 3 meters.
Explanation
For calculating the longest length of the casing and wrap, first, we need to calculate the GCF of 15 and 24, which is 3. The length of each piece will be 3 meters.
Problem 4
An artist has two canvases, one 15 cm wide and the other 24 cm wide. She wants to cut them into the longest possible equal strips, without any canvas left over. What should be the width of each strip?
The artist needs the longest strip of canvas GCF of 15 and 24 3 = 3 The longest width of each strip is 3 cm.
Explanation
To find the longest width of each strip of the two canvases, 15 cm and 24 cm wide, respectively, we have to find the GCF of 15 and 24, which is 3 cm. The longest width of each strip is 3 cm.
Problem 5
If the GCF of 15 and ‘b’ is 3, and the LCM is 120. Find ‘b’.
The value of ‘b’ is 24.
Explanation
GCF × LCM = product of the numbers
3 × 120 = 15 × b
360 = 15b
b = 360 ÷ 15 = 24
FAQs on the Greatest Common Factor of 15 and 24
1.What is the LCM of 15 and 24?
2.Is 15 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 24?
5.Are 15 and 24 prime numbers?
Important Glossaries for GCF of 15 and 24
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, 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 24 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 15 and 24 is 120.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 15 and 24 is 3, as it is their largest common factor that divides the numbers completely.
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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.
