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103 LearnersLast updated on September 11, 2025
GCF of 8 and 16
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 8 and 16.
What is the GCF of 8 and 16?
The greatest common factor of 8 and 16 is 8. 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 8 and 16?
To find the GCF of 8 and 16, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 8 and 16 by Using Listing of Factors
Steps to find the GCF of 8 and 16 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 8 = 1, 2, 4, 8.
Factors of 16 = 1, 2, 4, 8, 16.
Step 2: Now, identify the common factors of them. Common factors of 8 and 16: 1, 2, 4, 8.
Step 3: Choose the largest factor. The largest factor that both numbers have is 8. The GCF of 8 and 16 is 8.
GCF of 8 and 16 Using Prime Factorization
To find the GCF of 8 and 16 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 8: 8 = 2 × 2 × 2 = 2³
Prime Factors of 16: 16 = 2 × 2 × 2 × 2 = 2⁴
Step 2: Now, identify the common prime factors. The common prime factors are: 2 × 2 × 2 = 2³
Step 3: Multiply the common prime factors. 2³ = 8. The Greatest Common Factor of 8 and 16 is 8.
GCF of 8 and 16 Using Division Method or Euclidean Algorithm Method
Find the GCF of 8 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 8. 16 ÷ 8 = 2 (quotient), The remainder is calculated as 16 − (8×2) = 0.
The remainder is zero, so the divisor becomes the GCF. The GCF of 8 and 16 is 8.
Common Mistakes and How to Avoid Them in GCF of 8 and 16
Finding the GCF of 8 and 16 looks 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 8, 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 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, 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 8 and 16 Examples
Problem 1
There are 8 apples and 16 oranges. A vendor wants to pack them into boxes with the largest number of fruits in each box. How many fruits will be in each box?
We should find the GCF of 8 and 16. The GCF of 8 and 16 is 8.
There are 8 fruits in each box. 8 ÷ 8 = 1
16 ÷ 8 = 2
There will be 8 boxes, and each box gets 1 apple and 2 oranges.
Explanation
As the GCF of 8 and 16 is 8, the vendor can make boxes with 8 fruits each. Now divide 8 and 16 by 8. Each box gets 1 apple and 2 oranges.
Problem 2
A school wants to arrange 8 red balloons and 16 blue balloons in rows with the same number of balloons in each row, using the largest possible number of balloons per row. How many balloons will be in each row?
The GCF of 8 and 16 is 8. So each row will have 8 balloons.
Explanation
There are 8 red and 16 blue balloons. To find the total number of balloons in each row, we should find the GCF of 8 and 16. There will be 8 balloons in each row.
Problem 3
A painter has 8 meters of red ribbon and 16 meters of blue ribbon. She wants to cut both ribbons 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 8 and 16. The GCF of 8 and 16 is 8. The ribbon is 8 meters long.
Explanation
For calculating the longest length of the ribbon, first we need to calculate the GCF of 8 and 16, which is 8. The length of each piece of the ribbon will be 8 meters.
Problem 4
A carpenter has two wooden planks, one 8 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. The GCF of 8 and 16 is 8. The longest length of each piece is 8 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 8 cm and 16 cm, respectively, we have to find the GCF of 8 and 16, which is 8 cm. The longest length of each piece is 8 cm.
Problem 5
If the GCF of 8 and ‘b’ is 4, and the LCM is 32, find ‘b’.
The value of ‘b’ is 16.
Explanation
GCF × LCM = product of the numbers
4 × 32 = 8 × b
128 = 8b
b = 128 ÷ 8 = 16
FAQs on the Greatest Common Factor of 8 and 16
1.What is the LCM of 8 and 16?
2.Is 8 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 16?
5.Are 8 and 16 prime numbers?
Important Glossaries for GCF of 8 and 16
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, 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 16 are 2.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 16 is 16.
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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.
