Greatest Common Factor Of 72

GCF of 72 and 96

GCF of 72 and 96 is the largest possible number that divides 72 and 96 exactly without any residual. The factors of 72 and 96 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, ii, iii, four, 6, 8, 12, 16, 24, 32, 48, 96 respectively. There are 3 commonly used methods to detect the GCF of 72 and 96 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 72 and 96
2.	Listing of Methods
3.	Solved Examples
four.	FAQs

What is GCF of 72 and 96?

Reply: GCF of 72 and 96 is 24.

GCF of 72 and 96

Explanation:

The GCF of two non-zero integers, x(72) and y(96), is the greatest positive integer m(24) that divides both x(72) and y(96) without any residual.

Methods to Find GCF of 72 and 96

Let's look at the different methods for finding the GCF of 72 and 96.

Prime number Factorization Method
Listing Common Factors
Long Segmentation Method

GCF of 72 and 96 past Prime Factorization

GCF of 72 and 96 by Prime Factorization

Prime factorization of 72 and 96 is (2 × 2 × 2 × 3 × 3) and (ii × two × 2 × 2 × 2 × 3) respectively. As visible, 72 and 96 have common prime factors. Hence, the GCF of 72 and 96 is 2 × two × 2 × 3 = 24.

GCF of 72 and 96 by List Common Factors

Factors of 72: ane, ii, 3, 4, vi, 8, 9, 12, 18, 24, 36, 72
Factors of 96: 1, ii, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

In that location are eight common factors of 72 and 96, that are one, 2, 3, 4, 6, eight, 12, and 24. Therefore, the greatest common factor of 72 and 96 is 24.

GCF of 72 and 96 past Long Segmentation

GCF of 72 and 96 by Long Division

GCF of 72 and 96 is the divisor that we become when the residuum becomes 0 after doing long sectionalization repeatedly.

Step one: Divide 96 (larger number) past 72 (smaller number).
Step ii: Since the remainder ≠ 0, nosotros will split up the divisor of step 1 (72) by the remainder (24).
Step 3: Echo this process until the remainder = 0.

The corresponding divisor (24) is the GCF of 72 and 96.

☛ Also Check:

GCF of 49 and 98 = 49
GCF of 12 and threescore = 12
GCF of 9 and 16 = 1
GCF of 7 and 56 = 7
GCF of six and 36 = 6
GCF of 18 and thirty = half-dozen
GCF of 3 and nine = iii

GCF of 72 and 96 Examples

Case 1: Find the greatest number that divides 72 and 96 exactly.

Solution:

The greatest number that divides 72 and 96 exactly is their greatest common factor, i.eastward. GCF of 72 and 96.
⇒ Factors of 72 and 96:
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 96 = ane, two, three, 4, 6, 8, 12, 16, 24, 32, 48, 96
Therefore, the GCF of 72 and 96 is 24.
Example 2: Detect the GCF of 72 and 96, if their LCM is 288.

Solution:

∵ LCM × GCF = 72 × 96
⇒ GCF(72, 96) = (72 × 96)/288 = 24
Therefore, the greatest common factor of 72 and 96 is 24.
Example iii: The product of two numbers is 6912. If their GCF is 24, what is their LCM?

Solution:

Given: GCF = 24 and product of numbers = 6912
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 6912/24
Therefore, the LCM is 288.

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FAQs on GCF of 72 and 96

What is the GCF of 72 and 96?

The GCF of 72 and 96 is 24 . To calculate the GCF of 72 and 96, we need to factor each number (factors of 72 = 1, two, 3, four, six, viii, 9, 12, 18, 24, 36, 72; factors of 96 = 1, ii, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and cull the greatest factor that exactly divides both 72 and 96, i.eastward., 24.

How to Notice the GCF of 72 and 96 by Prime Factorization?

To find the GCF of 72 and 96, we will observe the prime factorization of the given numbers, i.due east. 72 = 2 × 2 × 2 × iii × iii; 96 = 2 × two × ii × 2 × two × 3.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 72 and 96. Hence, GCF(72, 96) = 2 × 2 × ii × three = 24
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 72, 96?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 72 and 96, i.eastward. GCF × LCM = 72 × 96.

If the GCF of 96 and 72 is 24, Discover its LCM.

GCF(96, 72) × LCM(96, 72) = 96 × 72
Since the GCF of 96 and 72 = 24
⇒ 24 × LCM(96, 72) = 6912
Therefore, LCM = 288
☛ GCF Calculator

What are the Methods to Find GCF of 72 and 96?

In that location are three commonly used methods to find the GCF of 72 and 96.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 72 and 96 by Long Division Method?

To detect the GCF of 72, 96 using long division method, 96 is divided past 72. The corresponding divisor (24) when remainder equals 0 is taken as GCF.