A day full of math games & activities. Find one near you.

GCF of 34 and 85

GCF of 34 and 85 is the largest possible number that divides 34 and 85 exactly without any remainder. The factors of 34 and 85 are 1, 2, 17, 34 and 1, 5, 17, 85 respectively. There are 3 commonly used methods to find the GCF of 34 and 85 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 34 and 85
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 34 and 85?

Answer: GCF of 34 and 85 is 17.

Explanation:

The GCF of two non-zero integers, x(34) and y(85), is the greatest positive integer m(17) that divides both x(34) and y(85) without any remainder.

Methods to Find GCF of 34 and 85

The methods to find the GCF of 34 and 85 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 34 and 85 by Listing Common Factors

Factors of 34: 1, 2, 17, 34
Factors of 85: 1, 5, 17, 85

There are 2 common factors of 34 and 85, that are 1 and 17. Therefore, the greatest common factor of 34 and 85 is 17.

GCF of 34 and 85 by Long Division

GCF of 34 and 85 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 85 (larger number) by 34 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (34) by the remainder (17).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (17) is the GCF of 34 and 85.

GCF of 34 and 85 by Prime Factorization

Prime factorization of 34 and 85 is (2 × 17) and (5 × 17) respectively. As visible, 34 and 85 have only one common prime factor i.e. 17. Hence, the GCF of 34 and 85 is 17.

☛ Also Check:

GCF of 34 and 85 Examples

Example 1: For two numbers, GCF = 17 and LCM = 170. If one number is 34, find the other number.

Solution:

Given: GCF (x, 34) = 17 and LCM (x, 34) = 170
∵ GCF × LCM = 34 × (x)
⇒ x = (GCF × LCM)/34
⇒ x = (17 × 170)/34
⇒ x = 85
Therefore, the other number is 85.
Example 2: Find the GCF of 34 and 85, if their LCM is 170.

Solution:

∵ LCM × GCF = 34 × 85
⇒ GCF(34, 85) = (34 × 85)/170 = 17
Therefore, the greatest common factor of 34 and 85 is 17.
Example 3: Find the greatest number that divides 34 and 85 exactly.

Solution:

The greatest number that divides 34 and 85 exactly is their greatest common factor, i.e. GCF of 34 and 85.
⇒ Factors of 34 and 85:
- Factors of 34 = 1, 2, 17, 34
- Factors of 85 = 1, 5, 17, 85
Therefore, the GCF of 34 and 85 is 17.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 34 and 85

What is the GCF of 34 and 85?

The GCF of 34 and 85 is 17. To calculate the GCF (Greatest Common Factor) of 34 and 85, we need to factor each number (factors of 34 = 1, 2, 17, 34; factors of 85 = 1, 5, 17, 85) and choose the greatest factor that exactly divides both 34 and 85, i.e., 17.

How to Find the GCF of 34 and 85 by Long Division Method?

To find the GCF of 34, 85 using long division method, 85 is divided by 34. The corresponding divisor (17) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 34, 85?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 34 and 85, i.e. GCF × LCM = 34 × 85.

What are the Methods to Find GCF of 34 and 85?

There are three commonly used methods to find the GCF of 34 and 85.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the GCF of 85 and 34 is 17, Find its LCM.

GCF(85, 34) × LCM(85, 34) = 85 × 34
Since the GCF of 85 and 34 = 17
⇒ 17 × LCM(85, 34) = 2890
Therefore, LCM = 170
☛ Greatest Common Factor Calculator

How to Find the GCF of 34 and 85 by Prime Factorization?

To find the GCF of 34 and 85, we will find the prime factorization of the given numbers, i.e. 34 = 2 × 17; 85 = 5 × 17.
⇒ Since 17 is the only common prime factor of 34 and 85. Hence, GCF (34, 85) = 17.
☛ Prime Number

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum