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100 LearnersLast updated on September 9, 2025
GCF of 17 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 17 and 34.
What is the GCF of 17 and 34?
The greatest common factor of 17 and 34 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 17 and 34?
To find the GCF of 17 and 34, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 17 and 34 by Using Listing of factors
Steps to find the GCF of 17 and 34 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 17 = 1, 17 Factors of 34 = 1, 2, 17, 34
Step 2: Now, identify the common factors of them Common factors of 17 and 34: 1, 17
Step 3: Choose the largest factor The largest factor that both numbers have is 17. The GCF of 17 and 34 is 17.
GCF of 17 and 34 Using Prime Factorization
To find the GCF of 17 and 34 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 17: 17 is a prime number, so its only prime factor is 17 Prime Factors of 34: 34 = 2 x 17
Step 2: Now, identify the common prime factors The common prime factor is: 17
Step 3: The GCF is the common prime factor The Greatest Common Factor of 17 and 34 is 17.
GCF of 17 and 34 Using Division Method or Euclidean Algorithm Method
Find the GCF of 17 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 34 by 17 34 ÷ 17 = 2 (quotient), The remainder is calculated as 34 − (17×2) = 0 The remainder is zero, so the divisor will become the GCF. The GCF of 17 and 34 is 17.
Common Mistakes and How to Avoid Them in GCF of 17 and 34
Finding the GCF of 17 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 17, students may mention 2, 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 17 and 34 Examples
Problem 1
A farmer has 17 apple trees and 34 orange trees. He wants to plant them in equal rows with the largest number of trees in each row. How many trees will be in each row?
We should find the GCF of 17 and 34 GCF of 17 and 34 is 17. There will be 17 equal rows. 17 ÷ 17 = 1 34 ÷ 17 = 2 There will be 17 trees in each row.
Explanation
As the GCF of 17 and 34 is 17, the farmer can make rows with 17 trees each.
Now divide 17 and 34 by 17.
Each row gets 1 apple tree and 2 orange trees.
Problem 2
A company has 17 laptops and 34 tablets. They want to distribute them equally among their employees, with the largest possible number of devices per employee. How many devices will each employee receive?
GCF of 17 and 34 is 17. So, each employee will receive 17 devices.
Explanation
There are 17 laptops and 34 tablets.
To find the total number of devices each employee can receive, we should find the GCF of 17 and 34.
There will be 17 devices for each employee.
Problem 3
A chef has 17 kg of sugar and 34 kg of flour. She wants to pack them into bags of equal weight, using the largest possible weight per bag. What should be the weight of each bag?
For calculating the largest equal weight, we have to calculate the GCF of 17 and 34.
The GCF of 17 and 34 is 17.
Each bag will weigh 17 kg.
Explanation
For calculating the largest weight of the bags, first, we need to calculate the GCF of 17 and 34, which is 17.
The weight of each bag will be 17 kg.
Problem 4
A decorator has two rolls of ribbon, one 17 meters long and the other 34 meters long. He wants to cut them into the longest possible equal pieces, without any ribbon left over. What should be the length of each piece?
The decorator needs the longest piece of ribbon. GCF of 17 and 34 is 17. The longest length of each piece is 17 meters.
Explanation
To find the longest length of each piece of the two rolls of ribbon, 17 meters and 34 meters, respectively, we have to find the GCF of 17 and 34, which is 17 meters.
The longest length of each piece is 17 meters.
Problem 5
If the GCF of 17 and ‘b’ is 17, and the LCM is 34, find ‘b’.
The value of ‘b’ is 34.
Explanation
GCF x LCM = product of the numbers
17 × 34
= 17 × b 578
= 17b b
= 578 ÷ 17 = 34
FAQs on the Greatest Common Factor of 17 and 34
1.What is the LCM of 17 and 34?
2.Is 17 a prime number?
3.What will be the GCF of any two consecutive numbers?
4.What is the prime factorization of 34?
5.Are 17 and 34 co-prime numbers?
Important Glossaries for GCF of 17 and 34
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 17 are 1 and 17.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 17 are 17, 34, 51, 68, 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 17 is divided by 5, the remainder is 2 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 17 and 34 is 34.
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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.
