Gcf Of 24 And 108

GCF of 108 and 24

GCF of 108 and 24 is the largest possible number that divides 108 and 24 exactly without whatsoever remainder. The factors of 108 and 24 are i, two, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are iii commonly used methods to find the GCF of 108 and 24 - Euclidean algorithm, prime number factorization, and long division.

1.	GCF of 108 and 24
ii.	List of Methods
iii.	Solved Examples
4.	FAQs

What is GCF of 108 and 24?

Respond: GCF of 108 and 24 is 12.

Explanation:

The GCF of ii non-zero integers, x(108) and y(24), is the greatest positive integer m(12) that divides both x(108) and y(24) without any remainder.

Methods to Detect GCF of 108 and 24

Let's look at the dissimilar methods for finding the GCF of 108 and 24.

• Using Euclid'southward Algorithm
• Prime Factorization Method
• Long Sectionalization Method

GCF of 108 and 24 by Euclidean Algorithm

Every bit per the Euclidean Algorithm, GCF(Ten, Y) = GCF(Y, X mod Y)
where X > Y and modern is the modulo operator.

Hither X = 108 and Y = 24

• GCF(108, 24) = GCF(24, 108 mod 24) = GCF(24, 12)
• GCF(24, 12) = GCF(12, 24 modernistic 12) = GCF(12, 0)
• GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, where 10 ≠ 0)

Therefore, the value of GCF of 108 and 24 is 12.

GCF of 108 and 24 past Prime number Factorization

Prime factorization of 108 and 24 is (2 × two × 3 × three × 3) and (2 × 2 × 2 × 3) respectively. As visible, 108 and 24 have common prime factors. Hence, the GCF of 108 and 24 is 2 × 2 × three = 12.

GCF of 108 and 24 past Long Division

GCF of 108 and 24 is the divisor that nosotros get when the remainder becomes 0 after doing long division repeatedly.

• Stride one: Divide 108 (larger number) past 24 (smaller number).
• Pace 2: Since the residual ≠ 0, we will divide the divisor of pace 1 (24) by the residuum (12).
• Step 3: Repeat this procedure until the remainder = 0.

The corresponding divisor (12) is the GCF of 108 and 24.

☛ Also Check:

• GCF of 36 and 84 = 12
• GCF of eighteen and fourteen = 2
• GCF of 8 and 36 = 4
• GCF of 32 and 81 = i
• GCF of 7 and 56 = 7
• GCF of 4 and 7 = 1
• GCF of 27 and thirty = 3

GCF of 108 and 24 Examples

1. Example 1: Discover the GCF of 108 and 24, if their LCM is 216.

   Solution:

   ∵ LCM × GCF = 108 × 24
   ⇒ GCF(108, 24) = (108 × 24)/216 = 12
   Therefore, the greatest common factor of 108 and 24 is 12.

2. Example 2: For two numbers, GCF = 12 and LCM = 216. If i number is 24, find the other number.

   Solution:

   Given: GCF (z, 24) = 12 and LCM (z, 24) = 216
   ∵ GCF × LCM = 24 × (z)
   ⇒ z = (GCF × LCM)/24
   ⇒ z = (12 × 216)/24
   ⇒ z = 108
   Therefore, the other number is 108.

3. Instance 3: Notice the greatest number that divides 108 and 24 exactly.

   Solution:

   The greatest number that divides 108 and 24 exactly is their greatest common factor, i.e. GCF of 108 and 24.
   ⇒ Factors of 108 and 24:

   • Factors of 108 = 1, two, iii, iv, 6, 9, 12, 18, 27, 36, 54, 108
   • Factors of 24 = one, 2, 3, 4, 6, 8, 12, 24

   Therefore, the GCF of 108 and 24 is 12.

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FAQs on GCF of 108 and 24

What is the GCF of 108 and 24?

The GCF of 108 and 24 is 12 . To summate the GCF (Greatest Common Cistron) of 108 and 24, we demand to cistron each number (factors of 108 = 1, 2, 3, 4, half-dozen, 9, 12, 18, 27, 36, 54, 108; factors of 24 = 1, 2, 3, 4, six, 8, 12, 24) and cull the greatest factor that exactly divides both 108 and 24, i.due east., 12.

How to Find the GCF of 108 and 24 by Long Division Method?

To notice the GCF of 108, 24 using long division method, 108 is divided by 24. The corresponding divisor (12) when residual equals 0 is taken equally GCF.

What are the Methods to Detect GCF of 108 and 24?

There are three commonly used methods to observe the GCF of 108 and 24.

• By Listing Mutual Factors
• Past Prime number Factorization
• By Long Division

What is the Relation Between LCM and GCF of 108, 24?

The following equation can be used to limited the relation between LCM and GCF of 108 and 24, i.due east. GCF × LCM = 108 × 24.

If the GCF of 24 and 108 is 12, Observe its LCM.

GCF(24, 108) × LCM(24, 108) = 24 × 108
Since the GCF of 24 and 108 = 12
⇒ 12 × LCM(24, 108) = 2592
Therefore, LCM = 216
☛ Greatest Mutual Factor Figurer

How to Discover the GCF of 108 and 24 by Prime number Factorization?

To discover the GCF of 108 and 24, we will find the prime factorization of the given numbers, i.e. 108 = 2 × ii × 3 × 3 × 3; 24 = ii × 2 × 2 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 108 and 24. Hence, GCF(108, 24) = 2 × 2 × 3 = 12
☛ What are Prime Numbers?

Gcf Of 24 And 108,

Source: https://www.cuemath.com/numbers/gcf-of-108-and-24/#:~:text=Answer%3A%20GCF%20of%20108%20and%2024%20is%2012.

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