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 schedule events. In this topic, we will learn about the GCF of 9 and 36.
The greatest common factor of 9 and 36 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 9 and 36, a few methods are described below -
Steps to find the GCF of 9 and 36 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 9 = 1, 3, 9.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 2: Now, identify the common factors of them Common factors of 9 and 36: 1, 3, 9.
Step 3: Choose the largest factor
The largest factor that both numbers have is 9.
The GCF of 9 and 36 is 9.
To find the GCF of 9 and 36 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number
Prime Factors of 9: 9 = 3 × 3 = 3²
Prime Factors of 36: 36 = 2 × 2 × 3 × 3 = 2² × 3²
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 9 and 36 is 9.
Find the GCF of 9 and 36 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 36 by 9 36 ÷ 9 = 4 (quotient),
The remainder is calculated as 36 - (9 × 4) = 0
The remainder is zero, so the divisor is the GCF.
The GCF of 9 and 36 is 9.
Finding GCF of 9 and 36 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 9 chocolate pastries and 36 vanilla pastries. She wants to pack them into boxes, with the largest number of pastries in each box. How many pastries will be in each box?
We should find the GCF of 9 and 36 GCF of 9 and 36 3² = 9.
There are 9 equal boxes 9 ÷ 9 = 1 36 ÷ 9 = 4
There will be 9 boxes, and each box gets 1 chocolate pastry and 4 vanilla pastries.
As the GCF of 9 and 36 is 9, the baker can make 9 boxes.
Now divide 9 and 36 by 9.
Each box gets 1 chocolate pastry and 4 vanilla pastries.
A concert organizer has 9 red flags and 36 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 9 and 36 3² = 9.
So each row will have 9 flags.
There are 9 red and 36 blue flags. To find the total number of flags in each row, we should find the GCF of 9 and 36. There will be 9 flags in each row.
A gardener has 9 meters of red hose and 36 meters of green hose. She wants to cut both hoses 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 9 and 36
The GCF of 9 and 36 3² = 9.
The hose is 9 meters long.
For calculating the longest length of the hose, first, we need to calculate the GCF of 9 and 36, which is 9. The length of each piece of the hose will be 9 meters.
A carpenter has two wooden planks, one 9 cm long and the other 36 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 9 and 36 3² = 9.
The longest length of each piece is 9 cm.
To find the longest length of each piece of the two wooden planks, 9 cm and 36 cm, respectively, we have to find the GCF of 9 and 36, which is 9 cm. The longest length of each piece is 9 cm.
If the GCF of 9 and ‘b’ is 9, and the LCM is 36, find ‘b’.
The value of ‘b’ is 36.
GCF × LCM = product of the numbers 9 × 36 = 9 × b
324 = 9b
b = 324 ÷ 9 = 36
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.