Summarize this article:
102 LearnersLast updated on September 18, 2025
GCF of 34 and 85
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 34 and 85.
What is the GCF of 34 and 85?
The greatest common factor of 34 and 85 is 17. 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 34 and 85?
To find the GCF of 34 and 85, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 34 and 85 by Using Listing of factors
Steps to find the GCF of 34 and 85 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 34 = 1, 2, 17, 34.
Factors of 85 = 1, 5, 17, 85.
Step 2: Now, identify the common factors of them Common factors of 34 and 85: 1, 17.
Step 3: Choose the largest factor The largest factor that both numbers have is 17. The GCF of 34 and 85 is 17.
GCF of 34 and 85 Using Prime Factorization
To find the GCF of 34 and 85 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime factors of 34: 34 = 2 × 17
Prime factors of 85: 85 = 5 × 17
Step 2: Now, identify the common prime factors The common prime factor is: 17
Step 3: Multiply the common prime factors 17 = 17. The Greatest Common Factor of 34 and 85 is 17.
GCF of 34 and 85 Using Division Method or Euclidean Algorithm Method
Find the GCF of 34 and 85 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 85 by 34 85 ÷ 34 = 2 (quotient),
The remainder is calculated as 85 − (34×2) = 17
The remainder is 17, not zero, so continue the process
Step 2: Now divide the previous divisor (34) by the previous remainder (17)
Divide 34 by 17 34 ÷ 17 = 2 (quotient), remainder = 34 − (17×2) = 0
The remainder is zero; the divisor will become the GCF.
The GCF of 34 and 85 is 17.
Common Mistakes and How to Avoid Them in GCF of 34 and 85
Finding GCF of 34 and 85 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 34, 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 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 odd number
Students may assume that GCF of two numbers will always be an odd number. But it's not true that a GCF can also be an even number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 34 and 85 Examples
Problem 1
A gardener has 34 tulips and 85 roses. She wants to create bouquets with the largest number of flowers in each bouquet, all equal. How many flowers will be in each bouquet?
We should find the GCF of 34 and 85 GCF of 34 and 85 17.
There are 17 equal bouquets 34 ÷ 17 = 2 85 ÷ 17 = 5
There will be 17 bouquets, and each bouquet gets 2 tulips and 5 roses.
Explanation
As the GCF of 34 and 85 is 17, the gardener can make 17 bouquets.
Now divide 34 and 85 by 17.
Each bouquet gets 2 tulips and 5 roses.
Problem 2
A teacher has 34 math books and 85 science books. She wants to arrange them in rows with the same number of books in each row, using the largest possible number of books per row. How many books will be in each row?
GCF of 34 and 85 17. So each row will have 17 books.
Explanation
There are 34 math and 85 science books.
To find the total number of books in each row, we should find the GCF of 34 and 85.
There will be 17 books in each row.
Problem 3
A tailor has 34 meters of silk fabric and 85 meters of cotton fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating longest equal length, we have to calculate the GCF of 34 and 85
The GCF of 34 and 85 17.
The fabric is 17 meters long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 34 and 85, which is 17.
The length of each piece of fabric will be 17 meters.
Problem 4
A chef has two loaves of bread, one 34 cm long and the other 85 cm long. He wants to cut them into the longest possible equal pieces, without any bread left over. What should be the length of each piece?
The chef needs the longest piece of bread GCF of 34 and 85 17.
The longest length of each piece is 17 cm.
Explanation
To find the longest length of each piece of the two loaves of bread, 34 cm and 85 cm, respectively, we have to find the GCF of 34 and 85, which is 17 cm.
The longest length of each piece is 17 cm.
Problem 5
If the GCF of 34 and ‘a’ is 17, and the LCM is 170, find ‘a’.
The value of ‘a’ is 85.
Explanation
GCF × LCM = product of the numbers
17 × 170 = 34 × a
2890 = 34a
a = 2890 ÷ 34 = 85
FAQs on the Greatest Common Factor of 34 and 85
1.What is the LCM of 34 and 85?
2.Is 34 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 85?
5.Are 34 and 85 prime numbers?
Important Glossaries for GCF of 34 and 85
- 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 5 are 5, 10, 15, 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 34 are 2 and 17.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 34 is divided by 9, the remainder is 7 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 34 and 85 is 170.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 34 and 85 will be 17, as it is their largest common factor that divides the numbers completely.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 34 and 85
![Important Math Links Icon]()
Next to GCF of 34 and 85
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.
