Summarize this article:
102 LearnersLast updated on October 16, 2025
GCF of 68 and 34
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 68 and 34.
What is the GCF of 68 and 34?
The greatest common factor of 68 and 34 is 34.
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.
How to find the GCF of 68 and 34?
To find the GCF of 68 and 34, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 68 and 34 by Using Listing of factors
Steps to find the GCF of 68 and 34 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 68 = 1, 2, 4, 17, 34, 68. Factors of 34 = 1, 2, 17, 34.
Step 2: Now, identify the common factors of them Common factors of 68 and 34: 1, 2, 17, 34.
Step 3: Choose the largest factor The largest factor that both numbers have is 34.
The GCF of 68 and 34 is 34.
GCF of 68 and 34 Using Prime Factorization
To find the GCF of 68 and 34 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 68: 68 = 2 x 2 x 17 = 2² x 17 Prime Factors of 34: 34 = 2 x 17.
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 17.
Step 3: Multiply the common prime factors 2 x 17 = 34.
The Greatest Common Factor of 68 and 34 is 34.
GCF of 68 and 34 Using Division Method or Euclidean Algorithm Method
Find the GCF of 68 and 34 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 68 by 34 68 ÷ 34 = 2 (quotient), The remainder is calculated as 68 - (34 x 2) = 0, The remainder is zero, so the divisor will become the GCF.
The GCF of 68 and 34 is 34.
Common Mistakes and How to Avoid Them in GCF of 68 and 34
Finding GCF of 68 and 34 looks simple, but students often make mistakes while calculating the GCF.
Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 68, students may mention 10, which is incorrect.
To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one.
To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers.
However, it does not affect the GCF, but it tells about the incomplete understanding of the factors.
Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse between factors and multiples.
In that confusion, sometimes they may write multiples instead of factors.
To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always an even number
Students may assume that the GCF of two numbers will always be an even number.
But it's not true that a GCF can also be an odd number.
To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 68 and 34 Examples
Problem 1
A gardener has 68 roses and 34 tulips. She wants to create bouquets with an equal number of flowers, using the largest possible number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 68 and 34 GCF of 68 and 34 2 x 17 = 34.
There are 34 equal bouquets 68 ÷ 34 = 2 34 ÷ 34 = 1.
There will be 34 bouquets, and each bouquet gets 2 roses and 1 tulip.
Explanation
As the GCF of 68 and 34 is 34, the gardener can make 34 bouquets.
Now divide 68 and 34 by 34.
Each bouquet gets 2 roses and 1 tulip.
Problem 2
A school has 68 desks and 34 chairs. They want to arrange them in rows with the same number of desks and chairs in each row, using the largest possible number of items per row. How many items will be in each row?
GCF of 68 and 34 2 x 17 = 34.
So each row will have 34 items.
Explanation
There are 68 desks and 34 chairs.
To find the total number of items in each row, we should find the GCF of 68 and 34.
There will be 34 items in each row.
Problem 3
A painter has 68 meters of red tape and 34 meters of blue tape. She wants to cut both tapes 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 68 and 34, The GCF of 68 and 34 2 x 17 = 34.
The tape is 34 meters long.
Explanation
For calculating the longest length of the tape first, we need to calculate the GCF of 68 and 34, which is 34.
The length of each piece of tape will be 34 meters.
Problem 4
A carpenter has two wooden planks, one 68 cm long and the other 34 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 68 and 34 2 x 17 = 34.
The longest length of each piece is 34 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 68 cm and 34 cm, respectively, we have to find the GCF of 68 and 34, which is 34 cm.
The longest length of each piece is 34 cm.
Problem 5
If the GCF of 68 and ‘b’ is 34, and the LCM is 136, find ‘b’.
The value of ‘b’ is 68.
Explanation
GCF x LCM = product of the numbers 34 x 136 = 68 x b 4624 = 68b b = 4624 ÷ 68 = 68
FAQs on the Greatest Common Factor of 68 and 34
1.What is the LCM of 68 and 34?
2.Is 68 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 34?
5.Are 68 and 34 prime numbers?
Important Glossaries for GCF of 68 and 34
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 34 are 1, 2, 17, and 34.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 68 are 2 and 17.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5, and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 68 and 34 is 68.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 68 and 34
![Important Math Links Icon]()
Next to GCF of 68 and 34
Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
