GCF the 15 and also 45 is the largest possible number the divides 15 and 45 exactly without any kind of remainder. The determinants of 15 and 45 are 1, 3, 5, 15 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used techniques to find the GCF that 15 and 45 - Euclidean algorithm, prime factorization, and also long division.

You are watching: Greatest common factor of 15 and 45

1.GCF of 15 and also 45
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF that 15 and 45 is 15.

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Explanation:

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


The approaches to uncover the GCF that 15 and 45 are defined below.

Prime administrate MethodLong division MethodUsing Euclid's Algorithm

GCF of 15 and also 45 by element Factorization

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

GCF the 15 and 45 by long Division

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GCF that 15 and also 45 is the divisor that we get when the remainder i do not care 0 after ~ doing long department repeatedly.

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

The equivalent divisor (15) is the GCF of 15 and 45.

GCF of 15 and also 45 by Euclidean Algorithm

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

Here X = 45 and Y = 15

GCF(45, 15) = GCF(15, 45 mode 15) = GCF(15, 0)GCF(15, 0) = 15 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

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

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GCF of 15 and also 45 Examples


Example 1: discover the GCF the 15 and 45, if your LCM is 45.

Solution:

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


Example 2: discover the best number that divides 15 and also 45 exactly.

Solution:

The greatest number the divides 15 and 45 exactly is their greatest common factor, i.e. GCF that 15 and also 45.⇒ components of 15 and 45:

Factors the 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, discover 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 45

What is the GCF that 15 and also 45?

The GCF of 15 and 45 is 15. To calculate the GCF the 15 and 45, we need to element each number (factors of 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 also 45, i.e., 15.

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

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

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

The adhering to equation have the right to be supplied to to express the relation in between Least common Multiple (LCM) and also GCF the 15 and 45, i.e. GCF × LCM = 15 × 45.

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

To discover the GCF of 15 and 45, us will uncover the element factorization the the given numbers, i.e. 15 = 3 × 5; 45 = 3 × 3 × 5.⇒ because 3, 5 are usual terms in the prime factorization that 15 and also 45. Hence, GCF(15, 45) = 3 × 5 = 15☛ element Numbers

What space the approaches to find GCF that 15 and also 45?

There are three typically used methods to uncover the GCF of 15 and also 45.

See more: Which Of The Following Should You Expect While Guarding Detainees? ?

By Euclidean AlgorithmBy lengthy DivisionBy element Factorization

How to find the GCF the 15 and also 45 by Long department Method?

To find the GCF that 15, 45 utilizing long division method, 45 is separated by 15. The equivalent divisor (15) as soon as remainder equals 0 is taken as GCF.