102 LearnersLast updated on August 5th, 2025
GCF of 15 and 64
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 15 and 64.
What is the GCF of 15 and 64?
The greatest common factor of 15 and 64 is 1. The largest divisor of two or more numbers is called the GCF of the numbers. 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 64?
To find the GCF of 15 and 64, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 15 and 64 by Using Listing of Factors
Steps to find the GCF of 15 and 64 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 15 = 1, 3, 5, 15.
Factors of 64 = 1, 2, 4, 8, 16, 32, 64.
Step 2: Now, identify the common factors Common factor of 15 and 64: 1.
Step 3: Choose the largest factor
The largest factor that both numbers have is 1.
The GCF of 15 and 64 is 1.
GCF of 15 and 64 Using Prime Factorization
To find the GCF of 15 and 64 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 15: 15 = 3 x 5
Prime Factors of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^6
Step 2: Identify the common prime factors
There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1.
GCF of 15 and 64 Using Division Method or Euclidean Algorithm Method
Find the GCF of 15 and 64 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 64 by 15 64 ÷ 15 = 4 (quotient),
The remainder is calculated as 64 - (15 x 4) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (15) by the previous remainder (4) 15 ÷ 4 = 3 (quotient), remainder = 15 - (4 x 3) = 3
Step 3: Continue the process 4 ÷ 3 = 1 (quotient), remainder = 4 - (3 x 1) = 1 3 ÷ 1 = 3 (quotient), remainder = 3 - (1 x 3) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 15 and 64 is 1.
Common Mistakes and How to Avoid Them in GCF of 15 and 64
Finding the GCF of 15 and 64 seems 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 a smaller 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 1 does not affect the GCF, it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse factors with multiples. In that confusion, 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 64 Examples
Problem 1
A gardener has 15 pots and 64 plants. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 15 and 64.
GCF of 15 and 64 is 1.
There will be only 1 item in each group.
Explanation
As the GCF of 15 and 64 is 1, the gardener can only make groups of 1 item each.
Problem 2
A school is organizing a science fair with 15 students and 64 projects. They want to arrange them into groups with the same number of students and projects in each group, using the largest possible number of students per group. How many students will be in each group?
GCF of 15 and 64 is 1.
So each group will have 1 student.
Explanation
With 15 students and 64 projects, the largest possible number of students per group is determined by the GCF of 15 and 64, which is 1. There will be 1 student in each group.
Problem 3
A tailor has 15 meters of red fabric and 64 meters of blue fabric. She 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 the longest equal length, we have to calculate the GCF of 15 and 64.
The GCF of 15 and 64 is 1.
Each piece of fabric will be 1 meter long.
Explanation
For determining the longest length of each fabric piece, first we calculate the GCF of 15 and 64, which is 1. The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 15 cm long and the other 64 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 15 and 64 is 1.
The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 15 cm and 64 cm respectively, we find the GCF of 15 and 64, which is 1 cm. The longest length of each piece is 1 cm.
Problem 5
If the GCF of 15 and ‘b’ is 1, and the LCM is 960, find ‘b’.
The value of ‘b’ is 64.
Explanation
GCF x LCM = product of the numbers 1 x 960 = 15 x b
960 = 15b
b = 960 ÷ 15 = 64
FAQs on the Greatest Common Factor of 15 and 64
1.What is the LCM of 15 and 64?
2.Is 15 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 64?
5.Are 15 and 64 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 15 and 64?
7.What are some fun ways kids in United States can practice GCF of 15 and 64 with numbers?
8.What role do numbers and GCF of 15 and 64 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 15 and 64 skills?
Important Glossaries for GCF of 15 and 64
- 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 64 are 2.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 64 is divided by 15, the remainder is 4.
- LCM: The smallest common multiple of two or more numbers is termed the LCM. For example, the LCM of 15 and 64 is 960.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 15 and 64 is 1, 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.
