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 28 and 44.
The greatest common factor of 28 and 44 is 4. 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 28 and 44, a few methods are described below -
Steps to find the GCF of 28 and 44 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 28 = 1, 2, 4, 7, 14, 28.
Factors of 44 = 1, 2, 4, 11, 22, 44.
Step 2: Now, identify the common factors of them Common factors of 28 and 44: 1, 2, 4.
Step 3: Choose the largest factor
The largest factor that both numbers have is 4.
The GCF of 28 and 44 is 4.
To find the GCF of 28 and 44 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 28: 28 = 2 x 2 x 7 = 2² x 7
Prime Factors of 44: 44 = 2 x 2 x 11 = 2² x 11
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 = 2²
Step 3: Multiply the common prime factors 2² = 4.
The Greatest Common Factor of 28 and 44 is 4.
Find the GCF of 28 and 44 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 44 by 28 44 ÷ 28 = 1 (quotient),
The remainder is calculated as 44 − (28×1) = 16
The remainder is 16, not zero, so continue the process
Step 2: Now divide the previous divisor (28) by the previous remainder (16) Divide 28 by 16 28 ÷ 16 = 1 (quotient), remainder = 28 − (16×1) = 12
Step 3: Continue the process Divide 16 by 12 16 ÷ 12 = 1 (quotient), remainder = 16 − (12×1) = 4
Step 4: Continue the process Divide 12 by 4 12 ÷ 4 = 3 (quotient), remainder = 12 − (4×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 28 and 44 is 4.
Finding GCF of 28 and 44 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 28 loaves of bread and 44 buns. 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 28 and 44 GCF of 28 and 44 2² = 4.
There are 4 equal groups 28 ÷ 4 = 7 44 ÷ 4 = 11
There will be 4 groups, and each group gets 7 loaves and 11 buns.
As the GCF of 28 and 44 is 4, the baker can make 4 groups. Now divide 28 and 44 by 4. Each group gets 7 loaves and 11 buns.
A gardener has 28 rose plants and 44 tulip plants. They want to arrange them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 28 and 44 2² = 4.
So each row will have 4 plants.
There are 28 rose and 44 tulip plants. To find the total number of plants in each row, we should find the GCF of 28 and 44. There will be 4 plants in each row.
A tailor has 28 meters of silk ribbon and 44 meters of cotton 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 28 and 44
The GCF of 28 and 44 2² = 4.
The ribbon is 4 meters long.
For calculating the longest length of the ribbon, first we need to calculate the GCF of 28 and 44, which is 4. The length of each piece of the ribbon will be 4 meters.
A carpenter has two wooden planks, one 28 cm long and the other 44 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 28 and 44 2² = 4.
The longest length of each piece is 4 cm.
To find the longest length of each piece of the two wooden planks, 28 cm and 44 cm, respectively, we have to find the GCF of 28 and 44, which is 4 cm. The longest length of each piece is 4 cm.
If the GCF of 28 and ‘b’ is 4, and the LCM is 308, find ‘b’.
The value of ‘b’ is 44.
GCF x LCM = product of the numbers 4 × 308 = 28 × b
1232 = 28b
b = 1232 ÷ 28 = 44
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.