103 LearnersLast updated on August 5th, 2025
GCF of 10 and 7
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 7.
What is the GCF of 10 and 7?
The greatest common factor of 10 and 7 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 10 and 7?
To find the GCF of 10 and 7, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 10 and 7 by Using Listing of Factors
Steps to find the GCF of 10 and 7 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 10 = 1, 2, 5, 10.
Factors of 7 = 1, 7.
Step 2: Now, identify the common factors of them
Common factor of 10 and 7: 1.
Step 3: Choose the largest factor
The largest factor that both numbers have is 1.
The GCF of 10 and 7 is 1.
GCF of 10 and 7 Using Prime Factorization
To find the GCF of 10 and 7 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 10: 10 = 2 × 5
Prime Factors of 7: 7 = 7 (7 is a prime number)
Step 2: Now, identify the common prime factors
There are no common prime factors.
Step 3: Multiply the common prime factors
Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 10 and 7 is 1.
GCF of 10 and 7 Using Division Method or Euclidean Algorithm Method
Find the GCF of 10 and 7 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 7
10 ÷ 7 = 1 (quotient), The remainder is calculated as 10 − (7 × 1) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (7) by the previous remainder (3)
Divide 7 by 3
7 ÷ 3 = 2 (quotient), remainder = 7 − (3 × 2) = 1
Step 3: 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 10 and 7 is 1.
Common Mistakes and How to Avoid Them in GCF of 10 and 7
Finding GCF of 10 and 7 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 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 7 Examples
Problem 1
A teacher has 10 apples and 7 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find GCF of 10 and 7.
GCF of 10 and 7 is 1.
There is only 1 group with 10 apples and 7 oranges.
Explanation
As the GCF of 10 and 7 is 1, the teacher can only make 1 group.
All the apples and oranges remain in that one group as they cannot be further divided into equal sets.
Problem 2
A school has 10 benches and 7 desks. They want to arrange them in rows with the same number of benches and desks in each row, using the largest possible number of benches and desks per row. How many benches and desks will be in each row?
GCF of 10 and 7 is 1.
So each row will have 1 bench and 1 desk.
Explanation
There are 10 benches and 7 desks.
To find the total number of benches and desks in each row, we should find the GCF of 10 and 7.
There will be 1 bench and 1 desk in each row.
Problem 3
A tailor has 10 meters of blue fabric and 7 meters of red 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 10 and 7
The GCF of 10 and 7 is 1.
Each piece of fabric is 1 meter long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 10 and 7 which is 1.
The length of each piece of the fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 10 cm long and the other 7 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 7 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, 10 cm and 7 cm, respectively, we have to find the GCF of 10 and 7, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 10 and ‘a’ is 1, and the LCM is 70, find ‘a’.
The value of ‘a’ is 7.
Explanation
GCF × LCM = product of the numbers
1 × 70 = 10 × a
70 = 10a
a = 70 ÷ 10 = 7
FAQs on the Greatest Common Factor of 10 and 7
1.What is the LCM of 10 and 7?
2.Is 10 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 7?
5.Are 10 and 7 prime numbers?
6.How can children in Thailand use numbers in everyday life to understand GCF of 10 and 7?
7.What are some fun ways kids in Thailand can practice GCF of 10 and 7 with numbers?
8.What role do numbers and GCF of 10 and 7 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve GCF of 10 and 7 skills?
Important Glossaries for GCF of 10 and 7
- 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 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.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 10 and 7 is 70.
- GCF: The l argest factor that commonly divides two or more numbers. For example, the GCF of 10 and 7 will be 1, 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.
