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GCF of 120 and 68

GCF of 120 and 68 is the largest possible number that divides 120 and 68 exactly without any remainder. The factors of 120 and 68 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 and 1, 2, 4, 17, 34, 68 respectively. There are 3 commonly used methods to find the GCF of 120 and 68 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 120 and 68
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 120 and 68?

Answer: GCF of 120 and 68 is 4.

Explanation:

The GCF of two non-zero integers, x(120) and y(68), is the greatest positive integer m(4) that divides both x(120) and y(68) without any remainder.

Methods to Find GCF of 120 and 68

Let's look at the different methods for finding the GCF of 120 and 68.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 120 and 68 by Listing Common Factors

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 68: 1, 2, 4, 17, 34, 68

There are 3 common factors of 120 and 68, that are 1, 2, and 4. Therefore, the greatest common factor of 120 and 68 is 4.

GCF of 120 and 68 by Long Division

GCF of 120 and 68 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 120 (larger number) by 68 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (68) by the remainder (52).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 120 and 68.

GCF of 120 and 68 by Prime Factorization

Prime factorization of 120 and 68 is (2 × 2 × 2 × 3 × 5) and (2 × 2 × 17) respectively. As visible, 120 and 68 have common prime factors. Hence, the GCF of 120 and 68 is 2 × 2 = 4.

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GCF of 120 and 68 Examples

Example 1: Find the greatest number that divides 120 and 68 exactly.

Solution:

The greatest number that divides 120 and 68 exactly is their greatest common factor, i.e. GCF of 120 and 68.
⇒ Factors of 120 and 68:
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
- Factors of 68 = 1, 2, 4, 17, 34, 68
Therefore, the GCF of 120 and 68 is 4.
Example 2: The product of two numbers is 8160. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 8160
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 8160/4
Therefore, the LCM is 2040.
Example 3: For two numbers, GCF = 4 and LCM = 2040. If one number is 120, find the other number.

Solution:

Given: GCF (y, 120) = 4 and LCM (y, 120) = 2040
∵ GCF × LCM = 120 × (y)
⇒ y = (GCF × LCM)/120
⇒ y = (4 × 2040)/120
⇒ y = 68
Therefore, the other number is 68.

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FAQs on GCF of 120 and 68

What is the GCF of 120 and 68?

The GCF of 120 and 68 is 4. To calculate the GCF of 120 and 68, we need to factor each number (factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120; factors of 68 = 1, 2, 4, 17, 34, 68) and choose the greatest factor that exactly divides both 120 and 68, i.e., 4.

If the GCF of 68 and 120 is 4, Find its LCM.

GCF(68, 120) × LCM(68, 120) = 68 × 120
Since the GCF of 68 and 120 = 4
⇒ 4 × LCM(68, 120) = 8160
Therefore, LCM = 2040
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 120, 68?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 120 and 68, i.e. GCF × LCM = 120 × 68.

How to Find the GCF of 120 and 68 by Long Division Method?

To find the GCF of 120, 68 using long division method, 120 is divided by 68. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

How to Find the GCF of 120 and 68 by Prime Factorization?

To find the GCF of 120 and 68, we will find the prime factorization of the given numbers, i.e. 120 = 2 × 2 × 2 × 3 × 5; 68 = 2 × 2 × 17.
⇒ Since 2, 2 are common terms in the prime factorization of 120 and 68. Hence, GCF(120, 68) = 2 × 2 = 4
☛ Prime Numbers

What are the Methods to Find GCF of 120 and 68?

There are three commonly used methods to find the GCF of 120 and 68.

By Listing Common Factors
By Long Division
By Prime Factorization

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