102 LearnersLast updated on August 13th, 2025
GCF of 15 and 16
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 16.
What is the GCF of 15 and 16?
The greatest common factor of 15 and 16 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 15 and 16?
To find the GCF of 15 and 16, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 15 and 16 by Using Listing of factors
Steps to find the GCF of 15 and 16 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 15 = 1, 3, 5, 15. Factors of 16 = 1, 2, 4, 8, 16.
Step 2: Now, identify the common factors of them Common factor of 15 and 16: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 15 and 16 is 1.
GCF of 15 and 16 Using Prime Factorization
To find the GCF of 15 and 16 using 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 16: 16 = 2 × 2 × 2 × 2 = 24
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Because there are no common prime factors, the GCF is 1. The Greatest Common Factor of 15 and 16 is 1.
GCF of 15 and 16 Using Division Method or Euclidean Algorithm Method
Find the GCF of 15 and 16 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 16 by 15 16 ÷ 15 = 1 (quotient), The remainder is calculated as 16 − (15×1) = 1 The remainder is 1, not zero, so continue the process
Step 2: Now divide the previous divisor (15) by the previous remainder (1) Divide 15 by 1 15 ÷ 1 = 15 (quotient), remainder = 15 − (1×15) = 0
The remainder is zero, the divisor becomes the GCF. The GCF of 15 and 16 is 1.
Common Mistakes and How to Avoid Them in GCF of 15 and 16
Finding GCF of 15 and 16 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 indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse 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 16 Examples
Problem 1
A gardener has 15 rose bushes and 16 tulip plants. She wants to plant them in rows with the same number of plants, using the largest possible number of plants per row. How many plants will be in each row?
We should find the GCF of 15 and 16 GCF of 15 and 16 is 1. There is only 1 plant in each row.
Explanation
As the GCF of 15 and 16 is 1, the gardener can make 1 plant in each row. Each row has 1 plant.
Problem 2
A chef has 15 apples and 16 oranges. She wants to arrange them in trays with the same number of fruits, using the largest possible number of fruits per tray. How many fruits will be in each tray?
GCF of 15 and 16 is 1. So each tray will have 1 fruit.
Explanation
There are 15 apples and 16 oranges. To find the total number of fruits in each tray, we should find the GCF of 15 and 16. There will be 1 fruit in each tray.
Problem 3
A tailor has 15 meters of red fabric and 16 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 16 The GCF of 15 and 16 is 1. The fabric is 1 meter long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 15 and 16, which is 1. The length of each piece of the fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 15 cm long and the other 16 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 16 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 16 cm, respectively, we have to find the GCF of 15 and 16, which is 1 cm. The longest length of each piece is 1 cm.
Problem 5
If the GCF of 15 and ‘a’ is 1, and the LCM is 240. Find ‘a’.
The value of ‘a’ is 16.
Explanation
GCF × LCM = product of the numbers
1 × 240 = 15 × a
240 = 15a
a = 240 ÷ 15 = 16
FAQs on the Greatest Common Factor of 15 and 16
1.What is the LCM of 15 and 16?
2.Is 15 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 16?
5.Are 15 and 16 prime numbers?
6.How can children in Philippines use numbers in everyday life to understand GCF of 15 and 16?
7.What are some fun ways kids in Philippines can practice GCF of 15 and 16 with numbers?
8.What role do numbers and GCF of 15 and 16 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve GCF of 15 and 16 skills?
Important Glossaries for GCF of 15 and 16
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.
- Co-prime Numbers: Two numbers are co-prime if their GCF is 1. For example, 15 and 16 are co-prime.
- 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 15 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 16 is divided by 15, the remainder is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 15 and 16 is 240.
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.
