Last updated on July 29th, 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, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 36 and 45.
The greatest common factor of 36 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 36 and 45, a few methods are described below:
Steps to find the GCF of 36 and 45 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 45 = 1, 3, 5, 9, 15, 45.
Step 2: Now, identify the common factors of them Common factors of 36 and 45: 1, 3, 9.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 9.
The GCF of 36 and 45 is 9.
To find the GCF of 36 and 45 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²
Prime Factors of 45: 45 = 3 x 3 x 5 = 3² x 5
Step 2: Now, identify the common prime factors
The common prime factors are: 3 x 3 = 3²
Step 3: Multiply the common prime factors 3² = 9.
The Greatest Common Factor of 36 and 45 is 9.
Find the GCF of 36 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 36 45 ÷ 36 = 1 (quotient),
The remainder is calculated as 45 − (36×1) = 9
The remainder is 9, not zero, so continue the process
Step 2: Now divide the previous divisor (36) by the previous remainder (9)
Divide 36 by 9 36 ÷ 9 = 4 (quotient), remainder = 36 − (9×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 36 and 45 is 9.
Finding GCF of 36 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 baker has 36 chocolate cupcakes and 45 vanilla cupcakes. She wants to pack them into boxes with the largest number of cupcakes in each box. How many cupcakes will be in each box?
We should find the GCF of 36 and 45. GCF of 36 and 45
3² = 9.
There are 9 equal boxes.
36 ÷ 9 = 4
45 ÷ 9 = 5
There will be 9 boxes, and each box gets 4 chocolate cupcakes and 5 vanilla cupcakes.
As the GCF of 36 and 45 is 9, the baker can make 9 boxes.
Now divide 36 and 45 by 9.
Each box gets 4 chocolate cupcakes and 5 vanilla cupcakes.
A garden has 36 rose bushes and 45 tulip bushes. The gardener wants to arrange them in rows with the same number of bushes in each row, using the largest possible number of bushes per row. How many bushes will be in each row?
GCF of 36 and 45
3² = 9.
So each row will have 9 bushes.
There are 36 rose bushes and 45 tulip bushes. To find the total number of bushes in each row, we should find the GCF of 36 and 45. There will be 9 bushes in each row.
A musician has 36 minutes of rock music and 45 minutes of jazz music. He wants to create playlists with the longest possible duration, using equal durations for each playlist. What should be the duration of each playlist?
For calculating the longest equal duration, we have to calculate the GCF of 36 and 45.
The GCF of 36 and 45
3² = 9.
The playlist duration is 9 minutes.
For calculating the longest duration for each playlist, first, we need to calculate the GCF of 36 and 45, which is 9. The duration of each playlist will be 9 minutes.
A carpenter has two wooden planks, one 36 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 36 and 45
3² = 9.
The longest length of each piece is 9 cm.
To find the longest length of each piece of the two wooden planks, 36 cm and 45 cm, respectively, we have to find the GCF of 36 and 45, which is 9 cm. The longest length of each piece is 9 cm.
If the GCF of 36 and ‘b’ is 9, and the LCM is 180. Find ‘b’.
The value of ‘b’ is 45.
GCF x LCM = product of the numbers
9 × 180 = 36 × b
1620 = 36b
b = 1620 ÷ 36 = 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.