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101 LearnersLast updated on September 17, 2025
GCF of 10 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 10 and 16.
What is the GCF of 10 and 16?
The greatest common factor of 10 and 16 is 2. 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 10 and 16?
To find the GCF of 10 and 16, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 10 and 16 by Using Listing of Factors
Steps to find the GCF of 10 and 16 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 10 = 1, 2, 5, 10. Factors of 16 = 1, 2, 4, 8, 16.
Step 2: Now, identify the common factors of them Common factors of 10 and 16: 1, 2.
Step 3: Choose the largest factor The largest factor that both numbers have is 2. The GCF of 10 and 16 is 2.
GCF of 10 and 16 Using Prime Factorization
To find the GCF of 10 and 16 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 10: 10 = 2 x 5
Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 24
Step 2: Now, identify the common prime factors The common prime factor is: 2
Step 3: Multiply the common prime factors 2 = 2. The Greatest Common Factor of 10 and 16 is 2.
GCF of 10 and 16 Using Division Method or Euclidean Algorithm Method
Find the GCF of 10 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 10 16 ÷ 10 = 1 (quotient),
The remainder is calculated as 16 − (10×1) = 6
The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (10) by the previous remainder (6)
Divide 10 by 6 10 ÷ 6 = 1 (quotient), remainder = 10 − (6×1) = 4 Continue the process
Step 3: Now divide the previous divisor (6) by the previous remainder (4)
Divide 6 by 4 6 ÷ 4 = 1 (quotient), remainder = 6 − (4×1) = 2
Continue the process
Step 4: Now divide the previous divisor (4) by the previous remainder (2)
Divide 4 by 2 4 ÷ 2 = 2 (quotient), remainder = 4 − (2×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 10 and 16 is 2.
Common Mistakes and How to Avoid Them in GCF of 10 and 16
Finding GCF of 10 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 10, students may mention 3 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 10 and 16 Examples
Problem 1
A gardener has 10 red roses and 16 white roses. She wants to bundle them into bouquets with an equal number of roses in each. How many roses will be in each bouquet?
We should find the GCF of 10 and 16 GCF of 10 and 16 2.
There are 2 equal bouquets 10 ÷ 2 = 5
16 ÷ 2 = 8
There will be 2 bouquets, and each bouquet gets 5 red roses and 8 white roses.
Explanation
As the GCF of 10 and 16 is 2, the gardener can make 2 bouquets.
Now divide 10 and 16 by 2. Each bouquet gets 5 red roses and 8 white roses.
Problem 2
A chef has 10 lemons and 16 oranges. He wants to arrange them in baskets with the same number of fruits in each. How many fruits will be in each basket?
GCF of 10 and 16 2.
So each basket will have 2 fruits.
Explanation
There are 10 lemons and 16 oranges.
To find the total number of fruits in each basket, we should find the GCF of 10 and 16.
There will be 2 fruits in each basket.
Problem 3
A tailor has 10 meters of fabric A and 16 meters of fabric B. 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 10 and 16
The GCF of 10 and 16 2.
The fabric piece is 2 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 10 and 16 which is 2. The length of each piece of fabric will be 2 meters.
Problem 4
A carpenter has two wooden planks, one 10 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 10 and 16 2.
The longest length of each piece is 2 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 10 cm and 16 cm, respectively.
We have to find the GCF of 10 and 16, which is 2 cm.
The longest length of each piece is 2 cm.
Problem 5
If the GCF of 10 and ‘a’ is 2, and the LCM is 80. Find ‘a’.
The value of ‘a’ is 16.
Explanation
GCF x LCM = product of the numbers
2 × 80 = 10 × a
160 = 10a
a = 160 ÷ 10 = 16
FAQs on the Greatest Common Factor of 10 and 16
1.What is the LCM of 10 and 16?
2.Is 10 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 16?
5.Are 10 and 16 prime numbers?
Important Glossaries for GCF of 10 and 16
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- 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, 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 factor of 10 is 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 6, the remainder is 4 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 10 and 16 is 80.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 10 and 16 is 2, 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.
