101 LearnersLast updated on August 5th, 2025
GCF of 10 and 45
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 to schedule events. In this topic, we will learn about the GCF of 10 and 45.
What is the GCF of 10 and 45?
The greatest common factor of 10 and 45 is 5. The largest divisor of two or more numbers is called the GCF of the numbers. 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 45?
To find the GCF of 10 and 45, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 10 and 45 by Using Listing of Factors
Steps to find the GCF of 10 and 45 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 10 = 1, 2, 5, 10.
Factors of 45 = 1, 3, 5, 9, 15, 45.
Step 2: Now, identify the common factors of them
Common factors of 10 and 45: 1, 5.
Step 3: Choose the largest factor
The largest factor that both numbers have is 5.
The GCF of 10 and 45 is 5.
GCF of 10 and 45 Using Prime Factorization
To find the GCF of 10 and 45 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 45: 45 = 3 x 3 x 5 = 3² x 5
Step 2: Now, identify the common prime factors
The common prime factor is: 5
Step 3: Multiply the common prime factors 5 = 5.
The Greatest Common Factor of 10 and 45 is 5.
GCF of 10 and 45 Using Division Method or Euclidean Algorithm Method
Find the GCF of 10 and 45 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 45 by 10 45 ÷ 10 = 4 (quotient),
The remainder is calculated as 45 − (10×4) = 5
The remainder is 5, not zero, so continue the process
Step 2: Now divide the previous divisor (10) by the previous remainder (5)
Divide 10 by 5 10 ÷ 5 = 2 (quotient), remainder = 10 − (5×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 10 and 45 is 5.
Common Mistakes and How to Avoid Them in GCF of 10 and 45
Finding the GCF of 10 and 45 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 4, 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 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 10 and 45 Examples
Problem 1
A gardener has 10 pots and 45 seeds. She wants to plant them in equal sets, with the largest number of items in each set. How many items will be in each set?
We should find the GCF of 10 and 45 GCF of 10 and 45
The common factor is 5.
There are 5 equal groups 10 ÷ 5 = 2 45 ÷ 5 = 9
There will be 5 groups, and each group gets 2 pots and 9 seeds.
Explanation
As the GCF of 10 and 45 is 5, the gardener can make 5 groups.
Now divide 10 and 45 by 5.
Each group gets 2 pots and 9 seeds.
Problem 2
A library has 10 fiction books and 45 non-fiction books. They want to arrange them in shelves with the same number of books on each shelf, using the largest possible number of books per shelf. How many books will be on each shelf?
GCF of 10 and 45 The common factor is 5.
So each shelf will have 5 books.
Explanation
There are 10 fiction and 45 non-fiction books.
To find the total number of books on each shelf, we should find the GCF of 10 and 45.
There will be 5 books on each shelf.
Problem 3
A tailor has 10 meters of red fabric and 45 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?
For calculating the longest equal length, we have to calculate the GCF of 10 and 45
The GCF of 10 and 45
The common factor is 5.
The fabric is 5 meters long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 10 and 45, which is 5.
The length of each piece of fabric will be 5 meters.
Problem 4
A carpenter has two wooden planks, one 10 cm long and the other 45 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 45
The common factor is 5.
The longest length of each piece is 5 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 10 cm and 45 cm, respectively, we have to find the GCF of 10 and 45, which is 5 cm.
The longest length of each piece is 5 cm.
Problem 5
If the GCF of 10 and ‘a’ is 5, and the LCM is 90. Find ‘a’.
The value of ‘a’ is 45.
Explanation
GCF x LCM = product of the numbers 5 × 90 = 10 × a
450 = 10a
a = 450 ÷ 10 = 45
FAQs on the Greatest Common Factor of 10 and 45
1.What is the LCM of 10 and 45?
2.Is 10 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 45?
5.Are 10 and 45 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 10 and 45?
7.What are some fun ways kids in India can practice GCF of 10 and 45 with numbers?
8.What role do numbers and GCF of 10 and 45 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 10 and 45 skills?
Important Glossaries for GCF of 10 and 45
- 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 45 are 3 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 the LCM. For example, the LCM of 10 and 45 is 90.
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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.
