GCF of 9 and also 24 is the largest feasible number the divides 9 and 24 exactly without any type of remainder. The factors of 9 and also 24 are 1, 3, 9 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There room 3 typically used methods to find the GCF the 9 and also 24 - prime factorization, long division, and Euclidean algorithm.

You are watching: What is the gcf of 24 and 9

1.GCF that 9 and also 24
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 9 and 24 is 3.

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Explanation:

The GCF of 2 non-zero integers, x(9) and also y(24), is the greatest positive essence m(3) the divides both x(9) and also y(24) without any type of remainder.


Let's look at the various methods because that finding the GCF that 9 and 24.

Long department MethodPrime factorization MethodListing typical Factors

GCF that 9 and also 24 by long Division

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GCF the 9 and also 24 is the divisor that we acquire when the remainder becomes 0 after ~ doing long division repeatedly.

Step 2: because the remainder ≠ 0, we will certainly divide the divisor of step 1 (9) by the remainder (6).Step 3: Repeat this procedure until the remainder = 0.

The matching divisor (3) is the GCF the 9 and also 24.

GCF of 9 and also 24 by prime Factorization

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Prime administrate of 9 and 24 is (3 × 3) and (2 × 2 × 2 × 3) respectively. As visible, 9 and also 24 have actually only one typical prime element i.e. 3. Hence, the GCF of 9 and also 24 is 3.

GCF the 9 and also 24 by Listing typical Factors

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

There space 2 typical factors of 9 and 24, that are 1 and also 3. Therefore, the greatest usual factor that 9 and 24 is 3.

☛ additionally Check:


GCF of 9 and 24 Examples


Example 1: discover the biggest number that divides 9 and also 24 exactly.

Solution:

The biggest number the divides 9 and also 24 specifically is your greatest common factor, i.e. GCF the 9 and also 24.⇒ components of 9 and 24:

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

Therefore, the GCF that 9 and 24 is 3.


Example 2: The product of two numbers is 216. If their GCF is 3, what is your LCM?

Solution:

Given: GCF = 3 and also product of numbers = 216∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 216/3Therefore, the LCM is 72.


Example 3: discover the GCF of 9 and also 24, if their LCM is 72.

Solution:

∵ LCM × GCF = 9 × 24⇒ GCF(9, 24) = (9 × 24)/72 = 3Therefore, the greatest usual factor that 9 and also 24 is 3.


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FAQs top top GCF the 9 and 24

What is the GCF that 9 and also 24?

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

If the GCF that 24 and also 9 is 3, find its LCM.

GCF(24, 9) × LCM(24, 9) = 24 × 9Since the GCF that 24 and also 9 = 3⇒ 3 × LCM(24, 9) = 216Therefore, LCM = 72☛ Greatest common Factor Calculator

How to uncover the GCF the 9 and 24 by element Factorization?

To uncover the GCF the 9 and 24, we will find the element factorization of the provided numbers, i.e. 9 = 3 × 3; 24 = 2 × 2 × 2 × 3.⇒ since 3 is the only usual prime element of 9 and also 24. Hence, GCF (9, 24) = 3.☛ prime Numbers

What is the Relation in between LCM and GCF of 9, 24?

The adhering to equation can be supplied to to express the relation between LCM (Least usual Multiple) and also GCF of 9 and 24, i.e. GCF × LCM = 9 × 24.

What space the methods to find GCF of 9 and 24?

There space three typically used methods to uncover the GCF of 9 and 24.

See more: Convert 21 Mm Equals How Many Inches Are 21 Millimeters, 21 Mm To In 21 Millimeters To Inches

By prime FactorizationBy lengthy DivisionBy Listing usual Factors

How to discover the GCF of 9 and 24 by Long department Method?

To uncover the GCF of 9, 24 making use of long department method, 24 is divided by 9. The matching divisor (3) once remainder equates to 0 is taken as GCF.