BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon103 Learners

Last updated on August 5th, 2025

Math Whiteboard Illustration

GCF of 10 and 7

Professor Greenline Explaining Math Concepts

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.

GCF of 10 and 7 for UAE Students
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Max Pointing Out Common Math Mistakes

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Listing Incorrect Factors

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Choosing the wrong common factor

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting to include 1 as a factor

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Using Multiples instead of factors

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Assuming GCF is always an even number

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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.

arrow-right
Max from BrightChamps Saying "Hey"
Hey!

Greatest Common Factor of 10 and 7 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

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.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

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.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

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.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

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.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

Problem 5

If the GCF of 10 and ‘a’ is 1, and the LCM is 70, find ‘a’.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

The value of ‘a’ is 7.

Explanation

GCF × LCM = product of the numbers

 

1 × 70 = 10 × a

 

70 = 10a

 

a = 70 ÷ 10 = 7

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Ray Thinking Deeply About Math Problems

FAQs on the Greatest Common Factor of 10 and 7

1.What is the LCM of 10 and 7?

The LCM of 10 and 7 is 70.

Math FAQ Answers Dropdown Arrow

2.Is 10 divisible by 2?

Yes, 10 is divisible by 2 because it is an even number.

Math FAQ Answers Dropdown Arrow

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself.

 

Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

Math FAQ Answers Dropdown Arrow

4.What is the prime factorization of 7?

The prime factorization of 7 is simply 7, as it is a prime number.

Math FAQ Answers Dropdown Arrow

5.Are 10 and 7 prime numbers?

No, 10 and 7 are not prime numbers because 10 has more than two factors, while 7 is a prime number.

Math FAQ Answers Dropdown Arrow

6.How can children in United Arab Emirates use numbers in everyday life to understand GCF of 10 and 7?

Numbers appear everywhere—from counting money to measuring ingredients. Kids in United Arab Emirates see how GCF of 10 and 7 helps solve real problems, making numbers meaningful beyond the classroom.

Math FAQ Answers Dropdown Arrow

7.What are some fun ways kids in United Arab Emirates can practice GCF of 10 and 7 with numbers?

Games like board games, sports scoring, or even cooking help children in United Arab Emirates use numbers naturally. These activities make practicing GCF of 10 and 7 enjoyable and connected to their world.

Math FAQ Answers Dropdown Arrow

8.What role do numbers and GCF of 10 and 7 play in helping children in United Arab Emirates develop problem-solving skills?

Working with numbers through GCF of 10 and 7 sharpens reasoning and critical thinking, preparing kids in United Arab Emirates for challenges inside and outside the classroom.

Math FAQ Answers Dropdown Arrow

9.How can families in United Arab Emirates create number-rich environments to improve GCF of 10 and 7 skills?

Families can include counting chores, measuring recipes, or budgeting allowances, helping children connect numbers and GCF of 10 and 7 with everyday activities.

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

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.
Math Teacher Background Image
Math Teacher Image

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.

Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
UAE - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom