GCF the 45 and also 75 is the largest possible number the divides 45 and also 75 specifically without any type of remainder. The components of 45 and also 75 room 1, 3, 5, 9, 15, 45 and also 1, 3, 5, 15, 25, 75 respectively. There room 3 commonly used methods to discover the GCF of 45 and also 75 - lengthy division, element factorization, and Euclidean algorithm.

You are watching: What is the gcf of 45 and 75

1.GCF the 45 and also 75
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF that 45 and 75 is 15.

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Explanation:

The GCF of two non-zero integers, x(45) and also y(75), is the biggest positive integer m(15) the divides both x(45) and also y(75) without any type of remainder.


The techniques to uncover the GCF the 45 and also 75 are described below.

Listing common FactorsPrime administrate MethodLong division Method

GCF of 45 and 75 through Listing typical Factors

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Factors of 45: 1, 3, 5, 9, 15, 45Factors the 75: 1, 3, 5, 15, 25, 75

There space 4 usual factors of 45 and also 75, that room 1, 3, 5, and also 15. Therefore, the greatest usual factor of 45 and 75 is 15.

GCF that 45 and also 75 by prime Factorization

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Prime administer of 45 and 75 is (3 × 3 × 5) and also (3 × 5 × 5) respectively. As visible, 45 and also 75 have usual prime factors. Hence, the GCF that 45 and 75 is 3 × 5 = 15.

GCF of 45 and also 75 by lengthy Division

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GCF the 45 and 75 is the divisor the we obtain when the remainder i do not care 0 after ~ doing long department repeatedly.

Step 2: because the remainder ≠ 0, we will certainly divide the divisor of action 1 (45) through the remainder (30).Step 3: Repeat this process until the remainder = 0.

The matching divisor (15) is the GCF of 45 and also 75.

☛ also Check:


GCF that 45 and 75 Examples


Example 1: discover the greatest number the divides 45 and 75 exactly.

Solution:

The greatest number that divides 45 and also 75 precisely is your greatest typical factor, i.e. GCF of 45 and 75.⇒ components of 45 and 75:

Factors that 45 = 1, 3, 5, 9, 15, 45Factors of 75 = 1, 3, 5, 15, 25, 75

Therefore, the GCF the 45 and 75 is 15.


Example 2: The product of two numbers is 3375. If their GCF is 15, what is your LCM?

Solution:

Given: GCF = 15 and also product of number = 3375∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 3375/15Therefore, the LCM is 225.


Example 3: For 2 numbers, GCF = 15 and also LCM = 225. If one number is 75, uncover the other number.

Solution:

Given: GCF (x, 75) = 15 and LCM (x, 75) = 225∵ GCF × LCM = 75 × (x)⇒ x = (GCF × LCM)/75⇒ x = (15 × 225)/75⇒ x = 45Therefore, the other number is 45.


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FAQs on GCF the 45 and 75

What is the GCF of 45 and also 75?

The GCF that 45 and also 75 is 15. To calculation the GCF that 45 and 75, we need to element each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 75 = 1, 3, 5, 15, 25, 75) and choose the greatest factor that specifically divides both 45 and also 75, i.e., 15.

What space the techniques to uncover GCF of 45 and also 75?

There room three frequently used approaches to find the GCF of 45 and also 75.

By element FactorizationBy long DivisionBy Listing usual Factors

If the GCF the 75 and 45 is 15, uncover its LCM.

GCF(75, 45) × LCM(75, 45) = 75 × 45Since the GCF of 75 and also 45 = 15⇒ 15 × LCM(75, 45) = 3375Therefore, LCM = 225☛ Greatest usual Factor Calculator

How to find the GCF that 45 and also 75 by prime Factorization?

To uncover the GCF that 45 and 75, we will discover the element factorization the the given numbers, i.e. 45 = 3 × 3 × 5; 75 = 3 × 5 × 5.⇒ because 3, 5 are typical terms in the prime factorization of 45 and also 75. Hence, GCF(45, 75) = 3 × 5 = 15☛ What are Prime Numbers?

What is the Relation in between LCM and also GCF of 45, 75?

The complying with equation have the right to be offered to to express the relation between LCM (Least usual Multiple) and also GCF that 45 and 75, i.e. GCF × LCM = 45 × 75.

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How to uncover the GCF that 45 and also 75 through Long division Method?

To discover the GCF that 45, 75 utilizing long division method, 75 is divided by 45. The equivalent divisor (15) once remainder amounts to 0 is taken together GCF.