Last updated on August 5th, 2025
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.
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.
To find the GCF of 10 and 45, a few methods are described below -
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If the GCF of 10 and ‘a’ is 5, and the LCM is 90. Find ‘a’.
The value of ‘a’ is 45.
GCF x LCM = product of the numbers 5 × 90 = 10 × a
450 = 10a
a = 450 ÷ 10 = 45
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.
: She loves to read number jokes and games.