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

GCF of 68 and 34

GCF of 68 and 34 is the largest possible number that divides 68 and 34 exactly without any remainder. The factors of 68 and 34 are 1, 2, 4, 17, 34, 68 and 1, 2, 17, 34 respectively. There are 3 commonly used methods to find the GCF of 68 and 34 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 68 and 34
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 68 and 34?

Answer: GCF of 68 and 34 is 34.

Explanation:

The GCF of two non-zero integers, x(68) and y(34), is the greatest positive integer m(34) that divides both x(68) and y(34) without any remainder.

Methods to Find GCF of 68 and 34

The methods to find the GCF of 68 and 34 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 68 and 34 by Long Division

GCF of 68 and 34 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 68 (larger number) by 34 (smaller number).
Step 2: Since the remainder = 0, the divisor (34) is the GCF of 68 and 34.

The corresponding divisor (34) is the GCF of 68 and 34.

GCF of 68 and 34 by Prime Factorization

Prime factorization of 68 and 34 is (2 × 2 × 17) and (2 × 17) respectively. As visible, 68 and 34 have common prime factors. Hence, the GCF of 68 and 34 is 2 × 17 = 34.

GCF of 68 and 34 by Listing Common Factors

Factors of 68: 1, 2, 4, 17, 34, 68
Factors of 34: 1, 2, 17, 34

There are 4 common factors of 68 and 34, that are 1, 2, 34, and 17. Therefore, the greatest common factor of 68 and 34 is 34.

☛ Also Check:

GCF of 68 and 34 Examples

Example 1: Find the GCF of 68 and 34, if their LCM is 68.

Solution:

∵ LCM × GCF = 68 × 34
⇒ GCF(68, 34) = (68 × 34)/68 = 34
Therefore, the greatest common factor of 68 and 34 is 34.
Example 2: For two numbers, GCF = 34 and LCM = 68. If one number is 68, find the other number.

Solution:

Given: GCF (z, 68) = 34 and LCM (z, 68) = 68
∵ GCF × LCM = 68 × (z)
⇒ z = (GCF × LCM)/68
⇒ z = (34 × 68)/68
⇒ z = 34
Therefore, the other number is 34.
Example 3: The product of two numbers is 2312. If their GCF is 34, what is their LCM?

Solution:

Given: GCF = 34 and product of numbers = 2312
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2312/34
Therefore, the LCM is 68.

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 68 and 34

What is the GCF of 68 and 34?

The GCF of 68 and 34 is 34. To calculate the greatest common factor of 68 and 34, we need to factor each number (factors of 68 = 1, 2, 4, 17, 34, 68; factors of 34 = 1, 2, 17, 34) and choose the greatest factor that exactly divides both 68 and 34, i.e., 34.

What is the Relation Between LCM and GCF of 68, 34?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 68 and 34, i.e. GCF × LCM = 68 × 34.

What are the Methods to Find GCF of 68 and 34?

There are three commonly used methods to find the GCF of 68 and 34.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 68 and 34 by Prime Factorization?

To find the GCF of 68 and 34, we will find the prime factorization of the given numbers, i.e. 68 = 2 × 2 × 17; 34 = 2 × 17.
⇒ Since 2, 17 are common terms in the prime factorization of 68 and 34. Hence, GCF(68, 34) = 2 × 17 = 34
☛ Prime Numbers

If the GCF of 34 and 68 is 34, Find its LCM.

GCF(34, 68) × LCM(34, 68) = 34 × 68
Since the GCF of 34 and 68 = 34
⇒ 34 × LCM(34, 68) = 2312
Therefore, LCM = 68
☛ GCF Calculator

How to Find the GCF of 68 and 34 by Long Division Method?

To find the GCF of 68, 34 using long division method, 68 is divided by 34. The corresponding divisor (34) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum