Gcf Of 45 And 54

GCF of 54 and 45

GCF of 54 and 45 is the largest possible number that divides 54 and 45 exactly without any remainder. The factors of 54 and 45 are ane, two, iii, 6, 9, 18, 27, 54 and ane, 3, five, 9, 15, 45 respectively. At that place are 3 commonly used methods to detect the GCF of 54 and 45 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 54 and 45
2.	Listing of Methods
three.	Solved Examples
4.	FAQs

What is GCF of 54 and 45?

Answer: GCF of 54 and 45 is 9.

Explanation:

The GCF of 2 non-zero integers, x(54) and y(45), is the greatest positive integer thousand(9) that divides both x(54) and y(45) without any residue.

Methods to Find GCF of 54 and 45

The methods to find the GCF of 54 and 45 are explained below.

• Listing Common Factors
• Using Euclid'south Algorithm
• Long Partition Method

GCF of 54 and 45 by Listing Common Factors

• Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
• Factors of 45: 1, 3, 5, 9, xv, 45

There are iii common factors of 54 and 45, that are 1, iii, and ix. Therefore, the greatest common factor of 54 and 45 is 9.

GCF of 54 and 45 by Euclidean Algorithm

Equally per the Euclidean Algorithm, GCF(Ten, Y) = GCF(Y, X mod Y)
where 10 > Y and mod is the modulo operator.

Here Ten = 54 and Y = 45

• GCF(54, 45) = GCF(45, 54 mod 45) = GCF(45, ix)
• GCF(45, 9) = GCF(ix, 45 mod 9) = GCF(nine, 0)
• GCF(9, 0) = nine (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 54 and 45 is 9.

GCF of 54 and 45 past Long Sectionalisation

GCF of 54 and 45 is the divisor that we get when the remainder becomes 0 after doing long sectionalisation repeatedly.

• Footstep 1: Separate 54 (larger number) by 45 (smaller number).
• Step ii: Since the residuum ≠ 0, we will dissever the divisor of pace ane (45) by the remainder (9).
• Step three: Echo this procedure until the balance = 0.

The corresponding divisor (nine) is the GCF of 54 and 45.

☛ Also Bank check:

• GCF of 12 and 9 = 3
• GCF of sixteen and 60 = four
• GCF of thirty and 60 = 30
• GCF of 54 and 32 = 2
• GCF of 4 and seven = one
• GCF of 24 and 64 = 8
• GCF of 45 and 81 = ix

GCF of 54 and 45 Examples

1. Instance 1: Find the greatest number that divides 54 and 45 exactly.

   Solution:

   The greatest number that divides 54 and 45 exactly is their greatest common factor, i.east. GCF of 54 and 45.
   ⇒ Factors of 54 and 45:

   • Factors of 54 = i, 2, 3, 6, 9, eighteen, 27, 54
   • Factors of 45 = 1, 3, v, 9, xv, 45

   Therefore, the GCF of 54 and 45 is 9.

2. Example 2: For 2 numbers, GCF = 9 and LCM = 270. If one number is 45, find the other number.

   Solution:

   Given: GCF (10, 45) = 9 and LCM (x, 45) = 270
   ∵ GCF × LCM = 45 × (10)
   ⇒ x = (GCF × LCM)/45
   ⇒ 10 = (9 × 270)/45
   ⇒ x = 54
   Therefore, the other number is 54.

3. Example three: Observe the GCF of 54 and 45, if their LCM is 270.

   Solution:

   ∵ LCM × GCF = 54 × 45
   ⇒ GCF(54, 45) = (54 × 45)/270 = 9
   Therefore, the greatest common factor of 54 and 45 is nine.

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FAQs on GCF of 54 and 45

What is the GCF of 54 and 45?

The GCF of 54 and 45 is 9 . To summate the GCF of 54 and 45, we need to factor each number (factors of 54 = i, 2, iii, six, 9, 18, 27, 54; factors of 45 = 1, 3, five, nine, xv, 45) and choose the greatest factor that exactly divides both 54 and 45, i.e., ix.

If the GCF of 45 and 54 is nine, Find its LCM.

GCF(45, 54) × LCM(45, 54) = 45 × 54
Since the GCF of 45 and 54 = 9
⇒ 9 × LCM(45, 54) = 2430
Therefore, LCM = 270
☛ GCF Calculator

How to Find the GCF of 54 and 45 by Prime Factorization?

To find the GCF of 54 and 45, we will find the prime factorization of the given numbers, i.e. 54 = 2 × iii × 3 × iii; 45 = 3 × 3 × 5.
⇒ Since 3, 3 are common terms in the prime factorization of 54 and 45. Hence, GCF(54, 45) = 3 × 3 = 9
☛ What are Prime number Numbers?

What are the Methods to Find GCF of 54 and 45?

There are iii ordinarily used methods to detect the GCF of 54 and 45.

• By Prime Factorization
• Past Long Division
• By List Mutual Factors

How to Find the GCF of 54 and 45 by Long Division Method?

To find the GCF of 54, 45 using long partitioning method, 54 is divided by 45. The corresponding divisor (ix) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 54, 45?

The following equation tin be used to express the relation between LCM (Least Common Multiple) and GCF of 54 and 45, i.eastward. GCF × LCM = 54 × 45.

Gcf Of 45 And 54,

Source: https://www.cuemath.com/numbers/gcf-of-54-and-45/

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