Last updated on July 30th, 2025
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 72 and 45.
The greatest common factor of 72 and 45 is 9. 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.
To find the GCF of 72 and 45, a few methods are described below
Steps to find the GCF of 72 and 45 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Factors of 45 = 1, 3, 5, 9, 15, 45.
Step 2: Now, identify the common factors of them:
Common factors of 72 and 45: 1, 3, 9.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 9.
The GCF of 72 and 45 is 9.
To find the GCF of 72 and 45 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 72: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
Prime Factors of 45: 45 = 3 × 3 × 5 = 3² × 5
Step 2: Now, identify the common prime factors:
The common prime factors are: 3 × 3 = 3²
Step 3: Multiply the common prime factors 3² = 9.
The Greatest Common Factor of 72 and 45 is 9.
Find the GCF of 72 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 72 by 45 72 ÷ 45 = 1 (quotient), The remainder is calculated as 72 − (45×1) = 27
The remainder is 27, not zero, so continue the process
Step 2: Now divide the previous divisor (45) by the previous remainder (27)
Divide 45 by 27 45 ÷ 27 = 1 (quotient), remainder = 45 − (27×1) = 18
Step 3: Continue with 27 and 18 27 ÷ 18 = 1 (quotient), remainder = 27 − (18×1) = 9
Step 4: Finally, divide 18 by 9 18 ÷ 9 = 2 (quotient), remainder = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 72 and 45 is 9.
Finding the GCF of 72 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 teacher has 72 markers and 45 notebooks. 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 the GCF of 72 and 45 GCF of 72 and 45 is 9.
There are 9 equal groups
72 ÷ 9 = 8
45 ÷ 9 = 5
There will be 9 groups, and each group gets 8 markers and 5 notebooks.
As the GCF of 72 and 45 is 9, the teacher can make 9 groups.
Now divide 72 and 45 by 9.
Each group gets 8 markers and 5 notebooks.
A school has 72 red chairs and 45 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 72 and 45 is 9. So each row will have 9 chairs.
There are 72 red and 45 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 72 and 45.
There will be 9 chairs in each row.
A tailor has 72 meters of red ribbon and 45 meters of blue ribbon. She wants to cut both ribbons 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 72 and 45
The GCF of 72 and 45 is 9.
The ribbon is 9 meters long.
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 72 and 45, which is 9.
The length of each piece of the ribbon will be 9 meters.
A carpenter has two wooden planks, one 72 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 72 and 45 is 9.
The longest length of each piece is 9 cm.
To find the longest length of each piece of the two wooden planks, 72 cm and 45 cm, respectively, we have to find the GCF of 72 and 45, which is 9 cm. The longest length of each piece is 9 cm.
If the GCF of 72 and ‘b’ is 9, and the LCM is 360. Find ‘b’.
The value of ‘b’ is 45.
GCF x LCM = product of the numbers
9 × 360 = 72 × b
3240 = 72b
b = 3240 ÷ 72 = 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.