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 6 and 35.
The greatest common factor of 6 and 35 is 1. 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 6 and 35, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
Steps to find the GCF of 6 and 35 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 6 = 1, 2, 3, 6.
Factors of 35 = 1, 5, 7, 35.
Step 2: Now, identify the common factors of them Common factors of 6 and 35: 1.
Step 3: Choose the largest factor
The largest factor that both numbers have is 1.
The GCF of 6 and 35 is 1.
To find the GCF of 6 and 35 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 6: 6 = 2 x 3
Prime Factors of 35: 35 = 5 x 7
Step 2: Now, identify the common prime factors
There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 6 and 35 is 1.
Find the GCF of 6 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 6 35 ÷ 6 = 5 (quotient),
The remainder is calculated as 35 − (6×5) = 5
The remainder is 5, not zero, so continue the process
Step 2: Now divide the previous divisor (6) by the previous remainder (5)
Divide 6 by 5 6 ÷ 5 = 1 (quotient), remainder = 6 − (5×1) = 1
The remainder is 1, not zero, so continue the process
Step 3: Now divide the previous divisor (5) by the previous remainder (1)
Divide 5 by 1 5 ÷ 1 = 5 (quotient), remainder = 5 − (1×5) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 6 and 35 is 1.
Finding the GCF of 6 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 park is being designed with a jogging track that is 6 meters wide and a walking path that is 35 meters wide. The designer wants to divide both paths into equal sections for landscaping, using the largest possible section length. What should be the length of each section?
We should find the GCF of 6 and 35 GCF of 6 and 35 is 1.
There are 1-meter equal sections. 6 ÷ 1 = 6
35 ÷ 1 = 35
Each section will be 1 meter long.
As the GCF of 6 and 35 is 1, the paths can be divided into 1-meter sections without any leftover.
A chef wants to use 6 eggs and 35 grams of flour to make the maximum number of identical batches of a recipe. What is the largest number of batches possible?
GCF of 6 and 35 is 1.
So, each batch will use 1 egg and 1 gram of flour.
The GCF of 6 eggs and 35 grams of flour is 1, so the chef can make 1 batch using 1 egg and 1 gram of flour per batch.
A farmer has 6 apple trees and 35 orange trees. He wants to plant them in rows with the same total number of trees in each row. What is the largest number of trees per row?
For calculating the largest equal number of trees per row, we have to calculate the GCF of 6 and 35, which is 1.
Each row will have 1 tree.
For organizing the trees, the GCF of 6 apple trees and 35 orange trees is 1. This means each row will have 1 tree.
A carpenter has two wooden rods, one 6 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 6 and 35 is 1.
The longest length of each piece is 1 cm.
To find the longest length of each piece of the two wooden rods, 6 cm and 35 cm, respectively, we have to find the GCF of 6 and 35, which is 1 cm. The longest length of each piece is 1 cm.
If the GCF of 6 and ‘b’ is 1, and the LCM is 210. Find ‘b’.
The value of ‘b’ is 35.
GCF x LCM = product of the numbers 1 × 210 = 6 × b
210 = 6b
b = 210 ÷ 6 = 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.