GCF the 15 and 45 is the largest possible number that divides 15 and also 45 precisely without any remainder. The components of 15 and 45 space 1, 3, 5, 15 and also 1, 3, 5, 9, 15, 45 respectively. There are 3 frequently used techniques to uncover the GCF of 15 and also 45 - Euclidean algorithm, prime factorization, and also long division.

You are watching: What is the gcf of 15 and 45

1.GCF the 15 and 45
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF of 15 and also 45 is 15.

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Explanation:

The GCF of 2 non-zero integers, x(15) and y(45), is the biggest positive integer m(15) the divides both x(15) and also y(45) without any remainder.


The techniques to find the GCF the 15 and also 45 are defined below.

Prime factorization MethodLong division MethodUsing Euclid's Algorithm

GCF the 15 and 45 by prime Factorization

Prime administrate of 15 and also 45 is (3 × 5) and also (3 × 3 × 5) respectively. As visible, 15 and also 45 have typical prime factors. Hence, the GCF of 15 and 45 is 3 × 5 = 15.

GCF the 15 and also 45 by long Division

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GCF that 15 and also 45 is the divisor the we get when the remainder becomes 0 ~ doing long department repeatedly.

Step 2: due to the fact that the remainder = 0, the divisor (15) is the GCF that 15 and 45.

The corresponding divisor (15) is the GCF that 15 and 45.

GCF the 15 and 45 by Euclidean Algorithm

As every the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode Y)where X > Y and also mod is the modulo operator.

Here X = 45 and also Y = 15

GCF(45, 15) = GCF(15, 45 mod 15) = GCF(15, 0)GCF(15, 0) = 15 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 15 and 45 is 15.

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GCF the 15 and 45 Examples


Example 1: find the GCF that 15 and also 45, if your LCM is 45.

Solution:

∵ LCM × GCF = 15 × 45⇒ GCF(15, 45) = (15 × 45)/45 = 15Therefore, the greatest usual factor that 15 and also 45 is 15.


Example 2: uncover the greatest number the divides 15 and 45 exactly.

Solution:

The biggest number the divides 15 and 45 specifically is your greatest typical factor, i.e. GCF that 15 and 45.⇒ components of 15 and 45:

Factors of 15 = 1, 3, 5, 15Factors of 45 = 1, 3, 5, 9, 15, 45

Therefore, the GCF the 15 and 45 is 15.


Example 3: For 2 numbers, GCF = 15 and also LCM = 45. If one number is 45, uncover the various other number.

Solution:

Given: GCF (z, 45) = 15 and LCM (z, 45) = 45∵ GCF × LCM = 45 × (z)⇒ z = (GCF × LCM)/45⇒ z = (15 × 45)/45⇒ z = 15Therefore, the various other number is 15.


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FAQs top top GCF of 15 and also 45

What is the GCF the 15 and 45?

The GCF the 15 and 45 is 15. To calculate the GCF the 15 and also 45, we require to factor each number (factors the 15 = 1, 3, 5, 15; components of 45 = 1, 3, 5, 9, 15, 45) and also choose the greatest aspect that precisely divides both 15 and 45, i.e., 15.

If the GCF the 45 and 15 is 15, find its LCM.

GCF(45, 15) × LCM(45, 15) = 45 × 15Since the GCF that 45 and 15 = 15⇒ 15 × LCM(45, 15) = 675Therefore, LCM = 45☛ Greatest common Factor Calculator

What is the Relation in between LCM and also GCF the 15, 45?

The complying with equation can be provided to refer the relation between Least common Multiple (LCM) and GCF that 15 and 45, i.e. GCF × LCM = 15 × 45.

How to discover the GCF of 15 and also 45 by element Factorization?

To find the GCF of 15 and 45, we will uncover the element factorization the the given numbers, i.e. 15 = 3 × 5; 45 = 3 × 3 × 5.⇒ since 3, 5 are common terms in the element factorization of 15 and 45. Hence, GCF(15, 45) = 3 × 5 = 15☛ prime Numbers

What room the approaches to uncover GCF of 15 and 45?

There space three commonly used methods to find the GCF that 15 and also 45.

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By Euclidean AlgorithmBy long DivisionBy element Factorization

How to uncover the GCF the 15 and 45 through Long department Method?

To find the GCF that 15, 45 making use of long department method, 45 is divided by 15. The corresponding divisor (15) as soon as remainder equates to 0 is taken together GCF.