GCF the 27 and 45 is the largest feasible number the divides 27 and also 45 precisely without any remainder. The factors of 27 and 45 space 1, 3, 9, 27 and 1, 3, 5, 9, 15, 45 respectively. There space 3 generally used techniques to discover the GCF of 27 and also 45 - lengthy division, element factorization, and Euclidean algorithm.

You are watching: What is the greatest common factor of 27 and 45

1.GCF the 27 and 45
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF that 27 and also 45 is 9.

*

Explanation:

The GCF of two non-zero integers, x(27) and y(45), is the biggest positive creature m(9) that divides both x(27) and y(45) without any type of remainder.


Let's look at the different methods for finding the GCF the 27 and also 45.

Long division MethodPrime factorization MethodListing usual Factors

GCF the 27 and also 45 by long Division

*

GCF of 27 and also 45 is the divisor that we obtain when the remainder becomes 0 after ~ doing long department repeatedly.

Step 2: because the remainder ≠ 0, we will divide the divisor of step 1 (27) by the remainder (18).Step 3: Repeat this procedure until the remainder = 0.

The matching divisor (9) is the GCF the 27 and also 45.

GCF that 27 and 45 by prime Factorization

*

Prime administrate of 27 and also 45 is (3 × 3 × 3) and also (3 × 3 × 5) respectively. Together visible, 27 and 45 have common prime factors. Hence, the GCF that 27 and 45 is 3 × 3 = 9.

GCF that 27 and also 45 by Listing usual Factors

Factors the 27: 1, 3, 9, 27Factors the 45: 1, 3, 5, 9, 15, 45

There room 3 typical factors of 27 and also 45, that space 1, 3, and also 9. Therefore, the greatest typical factor the 27 and also 45 is 9.

☛ also Check:


GCF of 27 and also 45 Examples


Example 1: For 2 numbers, GCF = 9 and LCM = 135. If one number is 45, find the other number.

Solution:

Given: GCF (x, 45) = 9 and also LCM (x, 45) = 135∵ GCF × LCM = 45 × (x)⇒ x = (GCF × LCM)/45⇒ x = (9 × 135)/45⇒ x = 27Therefore, the other number is 27.


Example 2: uncover the greatest number that divides 27 and also 45 exactly.

Solution:

The greatest number the divides 27 and also 45 precisely is your greatest typical factor, i.e. GCF that 27 and 45.⇒ factors of 27 and also 45:

Factors that 27 = 1, 3, 9, 27Factors that 45 = 1, 3, 5, 9, 15, 45

Therefore, the GCF the 27 and 45 is 9.


Example 3: find the GCF the 27 and 45, if their LCM is 135.

Solution:

∵ LCM × GCF = 27 × 45⇒ GCF(27, 45) = (27 × 45)/135 = 9Therefore, the greatest typical factor the 27 and also 45 is 9.


Show systems >

go come slidego to slidego to slide


*


Ready to view the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math difficulties in live classes and also become an expert at everything.

Book a complimentary Trial Class


FAQs ~ above GCF of 27 and also 45

What is the GCF the 27 and 45?

The GCF the 27 and 45 is 9. To calculate the GCF (Greatest typical Factor) that 27 and 45, we require to element each number (factors of 27 = 1, 3, 9, 27; components of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest variable that specifically divides both 27 and 45, i.e., 9.

If the GCF the 45 and 27 is 9, discover its LCM.

GCF(45, 27) × LCM(45, 27) = 45 × 27Since the GCF that 45 and 27 = 9⇒ 9 × LCM(45, 27) = 1215Therefore, LCM = 135☛ GCF Calculator

How to uncover the GCF the 27 and 45 by prime Factorization?

To uncover the GCF the 27 and 45, we will discover the prime factorization that the given numbers, i.e. 27 = 3 × 3 × 3; 45 = 3 × 3 × 5.⇒ because 3, 3 are usual terms in the element factorization of 27 and 45. Hence, GCF(27, 45) = 3 × 3 = 9☛ What is a prime Number?

What are the approaches to find GCF of 27 and 45?

There are three commonly used techniques to discover the GCF the 27 and also 45.

By Listing usual FactorsBy element FactorizationBy lengthy Division

How to find the GCF the 27 and 45 by Long division Method?

To discover the GCF that 27, 45 making use of long department method, 45 is separated by 27. The matching divisor (9) as soon as remainder amounts to 0 is taken as GCF.

See more: What Is The Answer To The Why Did Orgo Take His Girlfriend To The Cornfield

What is the Relation between LCM and also GCF of 27, 45?

The following equation have the right to be provided to express the relation between Least typical Multiple and GCF the 27 and also 45, i.e. GCF × LCM = 27 × 45.