102 LearnersLast updated on August 5th, 2025
GCF of 9 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 to schedule events. In this topic, we will learn about the GCF of 9 and 16.
What is the GCF of 9 and 16?
The greatest common factor of 9 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 9 and 16?
To find the GCF of 9 and 16, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 9 and 16 by Using Listing of factors
Steps to find the GCF of 9 and 16 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 9 = 1, 3, 9.
Factors of 16 = 1, 2, 4, 8, 16.
Step 2: Now, identify the common factors of them. Common factors of 9 and 16: 1.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 1.
The GCF of 9 and 16 is 1.
GCF of 9 and 16 Using Prime Factorization
To find the GCF of 9 and 16 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 9: 9 = 3 x 3 = 3²
Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 2⁴
Step 2: Now, identify the common prime factors: There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 9 and 16 is 1.
GCF of 9 and 16 Using Division Method or Euclidean Algorithm Method
Find the GCF of 9 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 9 16 ÷ 9 = 1 (quotient),
The remainder is calculated as 16 − (9×1) = 7
The remainder is 7, not zero, so continue the process
Step 2: Now divide the previous divisor (9) by the previous remainder (7) 9 ÷ 7 = 1 (quotient), remainder = 9 − (7×1) = 2
Step 3: Continue by dividing the previous divisor (7) by the remainder (2) 7 ÷ 2 = 3 (quotient), remainder = 7 − (2×3) = 1
Step 4: Finally, divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0
The remainder is zero, the last divisor will become the GCF.
The GCF of 9 and 16 is 1.
Common Mistakes and How to Avoid Them in GCF of 9 and 16
Finding the GCF of 9 and 16 seems simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 9, students may mention 6 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 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 more than 1
Students may assume that the GCF of two numbers will always be greater than 1. But it's not true; the GCF can also be 1, especially if the numbers are co-prime. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 9 and 16 Examples
Problem 1
A gardener has 9 rose bushes and 16 tulip bulbs. She wants to plant them in equal rows with the same number of plants in each row. How many plants will be in each row?
We should find the GCF of 9 and 16 GCF of 9 and 16 is 1.
There will be 1 plant in each row.
Explanation
As the GCF of 9 and 16 is 1, the gardener can plant 1 plant per row.
Each row will have 1 plant.
Problem 2
A chef has 9 apples and 16 oranges. She wants to prepare fruit baskets with the largest number of whole fruits in each basket. How many fruits will be in each basket?
GCF of 9 and 16 is 1. So each basket will have 1 fruit.
Explanation
There are 9 apples and 16 oranges. To find the total number of fruits in each basket, we should find the GCF of 9 and 16. There will be 1 fruit in each basket.
Problem 3
A tailor has 9 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 9 and 16
The GCF of 9 and 16 is 1.
The length of each piece is 1 meter.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 9 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 9 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 9 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, 9 cm and 16 cm, respectively, we have to find the GCF of 9 and 16, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 9 and ‘b’ is 1, and the LCM is 144. Find ‘b’.
The value of ‘b’ is 16.
Explanation
GCF x LCM = product of the numbers
1 × 144 = 9 × b
144 = 9b
b = 144 ÷ 9 = 16
FAQs on the Greatest Common Factor of 9 and 16
1.What is the LCM of 9 and 16?
2.Is 9 divisible by 3?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 16?
5.Are 9 and 16 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 9 and 16?
7.What are some fun ways kids in United States can practice GCF of 9 and 16 with numbers?
8.What role do numbers and GCF of 9 and 16 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 9 and 16 skills?
Important Glossaries for GCF of 9 and 16
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- 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, 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 9 are 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 16 is divided by 9, the remainder is 7, and the quotient is 1.
- Co-prime: Two numbers that have only 1 as their common factor. For example, 9 and 16 are co-prime.
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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.
