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 28 and 49.
The greatest common factor of 28 and 49 is 7. The largest divisor of two or more numbers is called the GCF of the numbers. 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 49, a few methods are described below:
Steps to find the GCF of 28 and 49 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 49 = 1, 7, 49.
Step 2: Now, identify the common factors of them.
Common factors of 28 and 49: 1, 7.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 7.
The GCF of 28 and 49 is 7.
To find the GCF of 28 and 49 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 49: 49 = 7 x 7 = 7²
Step 2: Now, identify the common prime factors.
The common prime factor is: 7
Step 3: Multiply the common prime factor. 7 = 7.
The Greatest Common Factor of 28 and 49 is 7.
Find the GCF of 28 and 49 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 49 by 28. 49 ÷ 28 = 1 (quotient),
The remainder is calculated as 49 - (28×1) = 21.
The remainder is 21, not zero, so continue the process.
Step 2: Now divide the previous divisor (28) by the previous remainder (21).
Divide 28 by 21. 28 ÷ 21 = 1 (quotient), remainder = 28 - (21×1) = 7.
Step 3: Now divide 21 by the remainder (7). 21 ÷ 7 = 3 (quotient), remainder = 21 - (7×3) = 0.
The remainder is zero, the divisor becomes the GCF.
The GCF of 28 and 49 is 7.
Finding the GCF of 28 and 49 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
A teacher has 28 apples and 49 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 28 and 49. GCF of 28 and 49 is 7.
There are 7 equal groups. 28 ÷ 7 = 4 49 ÷ 7 = 7
There will be 7 groups, and each group gets 4 apples and 7 oranges.
As the GCF of 28 and 49 is 7, the teacher can make 7 groups.
Now divide 28 and 49 by 7.
Each group gets 4 apples and 7 oranges.
A school has 28 red chairs and 49 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 28 and 49 is 7.
So each row will have 7 chairs.
There are 28 red and 49 blue chairs. To find the total number of chairs in each row, we should find the GCF of 28 and 49. There will be 7 chairs in each row.
A tailor has 28 meters of red ribbon and 49 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 28 and 49. The GCF of 28 and 49 is 7. The ribbon is 7 meters long.
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 28 and 49, which is 7.
The length of each piece of the ribbon will be 7 meters.
A carpenter has two wooden planks, one 28 cm long and the other 49 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 49 is 7.
The longest length of each piece is 7 cm.
To find the longest length of each piece of the two wooden planks, 28 cm and 49 cm, respectively, we have to find the GCF of 28 and 49, which is 7 cm. The longest length of each piece is 7 cm.
If the GCF of 28 and ‘a’ is 7, and the LCM is 196. Find ‘a’.
The value of ‘a’ is 49.
GCF x LCM = product of the numbers 7 × 196 = 28 × a
1372 = 28a
a = 1372 ÷ 28 = 49
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.