GCF the 24 and 72 is the largest possible number that divides 24 and also 72 specifically without any type of remainder. The determinants of 24 and also 72 room 1, 2, 3, 4, 6, 8, 12, 24 and also 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 frequently used approaches to discover the GCF that 24 and 72 - lengthy division, Euclidean algorithm, and prime factorization.

You are watching: Greatest common factor of 24 and 72

1.GCF the 24 and 72
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF the 24 and also 72 is 24.

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Explanation:

The GCF of two non-zero integers, x(24) and y(72), is the biggest positive integer m(24) that divides both x(24) and also y(72) without any kind of remainder.


Let's look in ~ the various methods because that finding the GCF that 24 and 72.

Prime administrate MethodLong division MethodListing common Factors

GCF the 24 and 72 by prime Factorization

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Prime administrate of 24 and also 72 is (2 × 2 × 2 × 3) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 24 and 72 have common prime factors. Hence, the GCF that 24 and also 72 is 2 × 2 × 2 × 3 = 24.

GCF the 24 and 72 by long Division

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GCF the 24 and also 72 is the divisor that we gain when the remainder i do not care 0 after doing long division repeatedly.

Step 2: because the remainder = 0, the divisor (24) is the GCF of 24 and also 72.

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

GCF the 24 and also 72 by Listing typical Factors

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Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24Factors that 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

There are 8 usual factors that 24 and 72, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the greatest usual factor that 24 and 72 is 24.

☛ also Check:


GCF that 24 and also 72 Examples


Example 1: For two numbers, GCF = 24 and LCM = 72. If one number is 72, uncover the various other number.

Solution:

Given: GCF (y, 72) = 24 and also LCM (y, 72) = 72∵ GCF × LCM = 72 × (y)⇒ y = (GCF × LCM)/72⇒ y = (24 × 72)/72⇒ y = 24Therefore, the various other number is 24.


Example 2: The product of 2 numbers is 1728. If your GCF is 24, what is your LCM?

Solution:

Given: GCF = 24 and product of number = 1728∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 1728/24Therefore, the LCM is 72.


Example 3: uncover the best number that divides 24 and also 72 exactly.

Solution:

The biggest number that divides 24 and also 72 specifically is their greatest common factor, i.e. GCF of 24 and also 72.⇒ components of 24 and 72:

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24Factors that 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Therefore, the GCF that 24 and also 72 is 24.


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FAQs on GCF of 24 and 72

What is the GCF that 24 and 72?

The GCF the 24 and also 72 is 24. To calculation the greatest common factor the 24 and also 72, we need to aspect each number (factors the 24 = 1, 2, 3, 4, 6, 8, 12, 24; components of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest aspect that specifically divides both 24 and 72, i.e., 24.

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

GCF(72, 24) × LCM(72, 24) = 72 × 24Since the GCF the 72 and 24 = 24⇒ 24 × LCM(72, 24) = 1728Therefore, LCM = 72☛ GCF Calculator

How to uncover the GCF the 24 and 72 by prime Factorization?

To find the GCF of 24 and also 72, we will discover the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 72 = 2 × 2 × 2 × 3 × 3.⇒ because 2, 2, 2, 3 are common terms in the prime factorization that 24 and 72. Hence, GCF(24, 72) = 2 × 2 × 2 × 3 = 24☛ prime Numbers

How to discover the GCF the 24 and also 72 by Long department Method?

To find the GCF that 24, 72 utilizing long department method, 72 is separated by 24. The matching divisor (24) when remainder amounts to 0 is taken together GCF.

What are the approaches to discover GCF of 24 and 72?

There space three commonly used approaches to find the GCF that 24 and 72.

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By prime FactorizationBy Listing common FactorsBy lengthy Division

What is the Relation between LCM and GCF of 24, 72?

The following equation can be provided to express the relation between Least typical Multiple and also GCF of 24 and also 72, i.e. GCF × LCM = 24 × 72.