GCF the 24 and 72 is the largest possible number that divides 24 and also 72 exactly without any remainder. The determinants of 24 and also 72 are 1, 2, 3, 4, 6, 8, 12, 24 and also 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There space 3 typically used approaches to uncover 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 of 24 and also 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 also y(72), is the best positive creature m(24) that divides both x(24) and also y(72) without any remainder.


Let's look in ~ the different methods for finding the GCF of 24 and also 72.

Prime administrate MethodLong department MethodListing typical Factors

GCF the 24 and 72 by prime Factorization

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

GCF that 24 and 72 by lengthy Division

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GCF that 24 and 72 is the divisor that we obtain when the remainder becomes 0 after doing long department repeatedly.

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

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

GCF that 24 and also 72 by Listing usual Factors

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Factors that 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 typical factors of 24 and 72, that room 1, 2, 3, 4, 6, 8, 12, and also 24. Therefore, the greatest common factor that 24 and also 72 is 24.

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GCF the 24 and also 72 Examples


Example 1: For 2 numbers, GCF = 24 and also LCM = 72. If one number is 72, find the other number.

Solution:

Given: GCF (y, 72) = 24 and 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 their GCF is 24, what is their LCM?

Solution:

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


Example 3: discover the biggest number the divides 24 and 72 exactly.

Solution:

The biggest number that divides 24 and also 72 specifically is your greatest typical factor, i.e. GCF that 24 and 72.⇒ determinants of 24 and also 72:

Factors that 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 of 24 and 72 is 24.


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FAQs on GCF of 24 and 72

What is the GCF that 24 and 72?

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

If the GCF that 72 and 24 is 24, discover its LCM.

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

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

To find the GCF that 24 and 72, us will find the prime factorization that 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 element factorization that 24 and 72. Hence, GCF(24, 72) = 2 × 2 × 2 × 3 = 24☛ prime Numbers

How to uncover the GCF the 24 and also 72 through Long department Method?

To find the GCF that 24, 72 utilizing long division method, 72 is split by 24. The equivalent divisor (24) as soon as remainder equals 0 is taken together GCF.

What are the techniques to find GCF the 24 and also 72?

There space three generally used methods to uncover the GCF the 24 and also 72.

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By prime FactorizationBy Listing usual FactorsBy lengthy Division

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

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