Last updated on July 31st, 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 22 and 55.
The greatest common factor of 22 and 55 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 are always positive.
To find the GCF of 22 and 55, a few methods are described below:
Steps to find the GCF of 22 and 55 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 22 = 1, 2, 11, 22
Factors of 55 = 1, 5, 11, 55
Step 2: Now, identify the common factors of them.
Common factors of 22 and 55: 1, 11
Step 3: Choose the largest factor
The largest factor that both numbers have is 11.
The GCF of 22 and 55 is 11.
To find the GCF of 22 and 55 using the 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 55: 55 = 5 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 55 is 11.
Find the GCF of 22 and 55 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 55 by 22 55 ÷ 22 = 2 (quotient)
The remainder is calculated as 55 − (22×2) = 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 55 is 11.
Finding GCF of 22 and 55 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 22 apples and 55 oranges. 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 22 and 55.
GCF of 22 and 55 is 11.
There are 11 equal groups.
22 ÷ 11 = 2
55 ÷ 11 = 5
There will be 11 groups, and each group gets 2 apples and 5 oranges.
As the GCF of 22 and 55 is 11, the teacher can make 11 groups.
Now divide 22 and 55 by 11.
Each group gets 2 apples and 5 oranges.
A school has 22 red chairs and 55 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 22 and 55 is 11. So each row will have 11 chairs.
There are 22 red and 55 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 22 and 55.
There will be 11 chairs in each row.
A tailor has 22 meters of red ribbon and 55 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 22 and 55.
The GCF of 22 and 55 is 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 55, which is 11. The length of each piece of the ribbon will be 11 meters.
A carpenter has two wooden planks, one 22 cm long and the other 55 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 55 is 11.
The longest length of each piece is 11 cm.
To find the longest length of each piece of the two wooden planks, 22 cm and 55 cm, respectively, we have to find the GCF of 22 and 55, which is 11 cm. The longest length of each piece is 11 cm.
If the GCF of 22 and ‘a’ is 11, and the LCM is 110. Find ‘a’.
The value of ‘a’ is 55.
GCF × LCM = product of the numbers
11 × 110 = 22 × a
1210 = 22a
a = 1210 ÷ 22 = 55
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.