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106 LearnersLast updated on September 20, 2025
GCF of 15 and 65
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 65.
What is the GCF of 15 and 65?
The greatest common factor of 15 and 65 is 5. 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 65?
To find the GCF of 15 and 65, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 15 and 65 by Using Listing of Factors
Steps to find the GCF of 15 and 65 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 15 = 1, 3, 5, 15.
Factors of 65 = 1, 5, 13, 65.
Step 2: Now, identify the common factors of them Common factors of 15 and 65: 1, 5.
Step 3: Choose the largest factor The largest factor that both numbers have is 5.
The GCF of 15 and 65 is 5.
GCF of 15 and 65 Using Prime Factorization
To find the GCF of 15 and 65 using 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 65: 65 = 5 x 13
Step 2: Now, identify the common prime factors The common prime factor is: 5
Step 3: Multiply the common prime factors 5 = 5
The Greatest Common Factor of 15 and 65 is 5.
GCF of 15 and 65 Using Division Method or Euclidean Algorithm Method
Find the GCF of 15 and 65 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 65 by 15 65 ÷ 15 = 4 (quotient),
The remainder is calculated as 65 − (15×4) = 5
The remainder is 5, not zero, so continue the process
Step 2: Now divide the previous divisor (15) by the previous remainder (5)
Divide 15 by 5 15 ÷ 5 = 3 (quotient), remainder = 15 − (5×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 15 and 65 is 5.
Common Mistakes and How to Avoid Them in GCF of 15 and 65
Finding the GCF of 15 and 65 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 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 15 and 65 Examples
Problem 1
A gardener has 15 rose bushes and 65 tulip plants. He wants to plant them in equal groups, with the largest number of plants in each group. How many plants will be in each group?
We should find GCF of 15 and 65 GCF of 15 and 65 5
There are 5 equal groups 15 ÷ 5 = 3 65 ÷ 5 = 13
There will be 5 groups, and each group gets 3 rose bushes and 13 tulip plants.
Explanation
As the GCF of 15 and 65 is 5, the gardener can make 5 groups.
Now divide 15 and 65 by 5.
Each group gets 3 rose bushes and 13 tulip plants.
Problem 2
A library has 15 copies of one book and 65 copies of another. They want to arrange them in shelves with the same number of books on each shelf, using the largest possible number of books per shelf. How many books will be in each shelf?
GCF of 15 and 65 5 So each shelf will have 5 books.
Explanation
There are 15 copies of one book and 65 copies of another.
To find the total number of books on each shelf, we should find the GCF of 15 and 65.
There will be 5 books in each shelf.
Problem 3
A chef has 15 kg of flour and 65 kg of sugar. She wants to pack them in bags of equal weight, using the heaviest possible weight for each bag. What should be the weight of each bag?
For calculating the heaviest equal weight, we have to calculate the GCF of 15 and 65
The GCF of 15 and 65 5
The weight of each bag is 5 kg.
Explanation
For calculating the heaviest weight of the bags, first, we need to calculate the GCF of 15 and 65 which is 5.
The weight of each bag will be 5 kg.
Problem 4
A carpenter has two wooden beams, one 15 cm long and the other 65 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 65 5
The longest length of each piece is 5 cm.
Explanation
To find the longest length of each piece of the two wooden beams, 15 cm and 65 cm, respectively.
We have to find the GCF of 15 and 65, which is 5 cm.
The longest length of each piece is 5 cm.
Problem 5
If the GCF of 15 and ‘b’ is 5, and the LCM is 195. Find ‘b’.
The value of ‘b’ is 65.
Explanation
GCF x LCM = product of the numbers
5 × 195 = 15 × b
975 = 15b
b = 975 ÷ 15 = 65
FAQs on the Greatest Common Factor of 15 and 65
1.What is the LCM of 15 and 65?
2.Is 15 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 65?
5.Are 15 and 65 prime numbers?
Important Glossaries for GCF of 15 and 65
- 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 5 are 5, 10, 15, 20, 25, 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 65 are 5 and 13.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 65 is divided by 15, the remainder is 5 and the quotient is 4.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 15 and 65 is 195.
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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.
