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 35.
The greatest common factor of 28 and 35 is 7. 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 35, a few methods are described below:
Steps to find the GCF of 28 and 35 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 35 = 1, 5, 7, 35.
Step 2: Now, identify the common factors of them Common factors of 28 and 35: 1, 7.
Step 3: Choose the largest factor The largest factor that both numbers have is 7.
The GCF of 28 and 35 is 7.
To find the GCF of 28 and 35 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 28: 28 = 2×2×7
Prime Factors of 35: 35 = 5×7
Step 2: Now, identify the common prime factors
The common prime factor is: 7
Step 3: Multiply the common prime factors 7
The Greatest Common Factor of 28 and 35 is 7.
Find the GCF of 28 and 35 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 35 by 28 35 ÷ 28 = 1 (quotient),
The remainder is calculated as 35 − (28×1) = 7
The remainder is 7, not zero, so continue the process
Step 2: Now divide the previous divisor (28) by the previous remainder (7)
Divide 28 by 7 28 ÷ 7 = 4 (quotient), remainder = 28 − (7×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 28 and 35 is 7.
Finding the GCF of 28 and 35 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 28 notebooks and 35 pens. 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 35 GCF of 28 and 35 is 7.
There are 7 equal groups
28 ÷ 7 = 4
35 ÷ 7 = 5
There will be 7 groups, and each group gets 4 notebooks and 5 pens.
As the GCF of 28 and 35 is 7, the teacher can make 7 groups.
Now divide 28 and 35 by 7.
Each group gets 4 notebooks and 5 pens.
A school has 28 red chairs and 35 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 35 is 7. So each row will have 7 chairs.
There are 28 red and 35 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 28 and 35.
There will be 7 chairs in each row.
A tailor has 28 meters of red ribbon and 35 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 35
The GCF of 28 and 35 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 35, 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 35 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 35 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 35 cm, respectively. We have to find the GCF of 28 and 35, 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 140. Find ‘a’.
The value of ‘a’ is 35.
GCF × LCM = product of the numbers
7 × 140 = 28 × a
980 = 28a
a = 980 ÷ 28 = 35
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.