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 the items equally, to group or arrange items and schedule events. In this topic, we will learn about the GCF of 22 and 33.
The greatest common factor of 22 and 33 is 11. 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, which are always positive.
To find the GCF of 22 and 33, a few methods are described below:
Steps to find the GCF of 22 and 33 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 22 = 1, 2, 11, 22.
Factors of 33 = 1, 3, 11, 33.
Step 2: Now, identify the common factors of them.
Common factors of 22 and 33: 1, 11.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 11.
The GCF of 22 and 33 is 11.
To find the GCF of 22 and 33 using Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number
Prime Factors of 22: 22 = 2 x 11
Prime Factors of 33: 33 = 3 x 11
Step 2: Now, identify the common prime factors.
The common prime factor is: 11
Step 3: Multiply the common prime factors.
The Greatest Common Factor of 22 and 33 is 11.
Find the GCF of 22 and 33 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 33 by 22 33 ÷ 22 = 1 (quotient), The remainder is calculated as 33 − (22×1) = 11
The remainder is 11, not zero, so continue the process
Step 2: Now divide the previous divisor (22) by the previous remainder (11)
Divide 22 by 11 22 ÷ 11 = 2 (quotient), remainder = 22 − (11×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 22 and 33 is 11.
Finding GCF of 22 and 33 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 22 red tulips and 33 yellow tulips. She wants to arrange them in bouquets with the largest number of tulips in each bouquet. How many tulips will be in each bouquet?
We should find GCF of 22 and 33 GCF of 22 and 33 11. There are 11 bouquets 22 ÷ 11 = 2 33 ÷ 11 = 3 There will be 11 bouquets, and each bouquet gets 2 red tulips and 3 yellow tulips.
As the GCF of 22 and 33 is 11, the gardener can make 11 bouquets. Now divide 22 and 33 by 11. Each bouquet gets 2 red tulips and 3 yellow tulips.
A company has 22 computers and 33 monitors. They want to organize them into workstations with the same number of computers and monitors in each workstation, using the largest possible number of items per workstation. How many items will be in each workstation?
GCF of 22 and 33 11. So each workstation will have 11 items.
There are 22 computers and 33 monitors.
To find the total number of items in each workstation, we should find the GCF of 22 and 33.
There will be 11 items in each workstation.
A baker has 22 meters of chocolate ribbon and 33 meters of vanilla 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 longest equal length, we have to calculate the GCF of 22 and 33
The GCF of 22 and 33 11.
The ribbon is 11 meters long.
For calculating the longest length of the ribbon first we need to calculate the GCF of 22 and 33 which is 11. The length of each piece of the ribbon will be 11 meters.
A carpenter has two wooden beams, one 22 cm long and the other 33 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 22 and 33 is 11.
The longest length of each piece is 11 cm.
To find the longest length of each piece of the two wooden beams, 22 cm and 33 cm, respectively.
We have to find the GCF of 22 and 33, which is 11 cm.
The longest length of each piece is 11 cm.
If the GCF of 22 and ‘b’ is 11, and the LCM is 66. Find ‘b’.
The value of ‘b’ is 33.
GCF x LCM = product of the numbers
11 × 66 = 22 × b
726 = 22b
b = 726 ÷ 22 = 33
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.