Summarize this article:
104 LearnersLast updated on September 12, 2025
GCF of 3 and 10
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 3 and 10.
What is the GCF of 3 and 10?
The greatest common factor of 3 and 10 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 3 and 10?
To find the GCF of 3 and 10, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 3 and 10 by Using Listing of Factors
Steps to find the GCF of 3 and 10 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 3 = 1, 3. Factors of 10 = 1, 2, 5, 10.
Step 2: Now, identify the common factors of them Common factors of 3 and 10: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 3 and 10 is 1.
GCF of 3 and 10 Using Prime Factorization
To find the GCF of 3 and 10 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 3: 3 = 3
Prime Factors of 10: 10 = 2 x 5
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 3 and 10 is 1.
GCF of 3 and 10 Using Division Method or Euclidean Algorithm Method
Find the GCF of 3 and 10 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 10 by 3 10 ÷ 3 = 3 (quotient), The remainder is calculated as 10 − (3×3) = 1 The remainder is 1, not zero, so continue the process
Step 2: Now divide the previous divisor (3) by the previous remainder (1) Divide 3 by 1 3 ÷ 1 = 3 (quotient), remainder = 3 − (1×3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 3 and 10 is 1.
Common Mistakes and How to Avoid Them in GCF of 3 and 10
Finding the GCF of 3 and 10 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 a factor that is not common to both numbers. To avoid this confusion, students should list all the common factors and identify the correct ones.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. While it does not affect the GCF when numbers are co-prime, it reflects an incomplete understanding of 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 greater than 1
Students may assume that the GCF of two numbers will always be greater than 1. But it's not true if the numbers are co-prime. To avoid this, students should focus on common factors rather than assumptions about the GCF's size.
Greatest Common Factor of 3 and 10 Examples
Problem 1
A gardener has 3 apple trees and 10 orange trees. She wants to plant them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
We should find the GCF of 3 and 10. The GCF of 3 and 10 is 1. There will be 1 tree in each row.
Explanation
As the GCF of 3 and 10 is 1, the gardener can plant 1 tree per row to ensure equal rows.
Problem 2
A baker has 3 cakes and 10 pastries. He wants to pack them in boxes with the same number of items in each box, using the largest possible number of items per box. How many items will be in each box?
The GCF of 3 and 10 is 1. So, each box will have 1 item.
Explanation
There are 3 cakes and 10 pastries. To find the total number of items in each box, we should find the GCF of 3 and 10. There will be 1 item in each box.
Problem 3
A tailor has 3 meters of red fabric and 10 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?
To calculate the longest equal length, we have to calculate the GCF of 3 and 10. The GCF of 3 and 10 is 1. The fabric pieces will be 1 meter long.
Explanation
For calculating the longest length of the fabric pieces, first, we need to calculate the GCF of 3 and 10, which is 1. The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 3 cm long and the other 10 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 3 and 10 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, 3 cm and 10 cm, respectively, we have to find the GCF of 3 and 10, which is 1 cm. The longest length of each piece is 1 cm.
Problem 5
If the GCF of 3 and ‘b’ is 1, and the LCM is 30, find ‘b’.
The value of ‘b’ is 10.
Explanation
GCF x LCM = product of the numbers
1 × 30 = 3 × b
30 = 3b
b = 30 ÷ 3 = 10
FAQs on the Greatest Common Factor of 3 and 10
1.What is the LCM of 3 and 10?
2.Is 3 a prime number?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 10?
5.Are 3 and 10 co-prime numbers?
Important Glossaries for GCF of 3 and 10
- 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 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 10 are 2 and 5.
- 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.
- Co-prime: Two numbers are co-prime if their greatest common factor is 1. For example, 3 and 10 are co-prime because their GCF is 1.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 3 and 10
![Important Math Links Icon]()
Next to GCF of 3 and 10
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.
