GCF the 75 and also 90 is the largest possible number that divides 75 and also 90 exactly without any type of remainder. The components of 75 and also 90 are 1, 3, 5, 15, 25, 75 and also 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There room 3 frequently used approaches to find the GCF of 75 and also 90 - lengthy division, Euclidean algorithm, and prime factorization.

You are watching: Greatest common factor of 75 and 90

1.GCF that 75 and 90
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF that 75 and also 90 is 15.

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Explanation:

The GCF of two non-zero integers, x(75) and y(90), is the best positive integer m(15) the divides both x(75) and also y(90) without any kind of remainder.


The methods to find the GCF the 75 and 90 are described below.

Listing typical FactorsPrime factorization MethodLong division Method

GCF of 75 and 90 by Listing usual Factors

Factors of 75: 1, 3, 5, 15, 25, 75Factors that 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There space 4 usual factors of 75 and also 90, that space 1, 3, 5, and also 15. Therefore, the greatest typical factor the 75 and 90 is 15.

GCF the 75 and 90 by prime Factorization

Prime factorization of 75 and also 90 is (3 × 5 × 5) and also (2 × 3 × 3 × 5) respectively. As visible, 75 and 90 have usual prime factors. Hence, the GCF of 75 and also 90 is 3 × 5 = 15.

GCF the 75 and also 90 by long Division

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GCF of 75 and 90 is the divisor that we obtain when the remainder becomes 0 ~ doing long division repeatedly.

Step 2: since the remainder ≠ 0, we will certainly divide the divisor of action 1 (75) through the remainder (15).Step 3: Repeat this process until the remainder = 0.

The matching divisor (15) is the GCF of 75 and also 90.

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GCF that 75 and 90 Examples


Example 1: The product of 2 numbers is 6750. If their GCF is 15, what is your LCM?

Solution:

Given: GCF = 15 and also product of number = 6750∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 6750/15Therefore, the LCM is 450.


Example 2: uncover the greatest number that divides 75 and also 90 exactly.

Solution:

The biggest number that divides 75 and also 90 specifically is their greatest typical factor, i.e. GCF of 75 and also 90.⇒ determinants of 75 and also 90:

Factors the 75 = 1, 3, 5, 15, 25, 75Factors that 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Therefore, the GCF the 75 and also 90 is 15.


Example 3: For 2 numbers, GCF = 15 and LCM = 450. If one number is 90, discover the other number.

Solution:

Given: GCF (x, 90) = 15 and also LCM (x, 90) = 450∵ GCF × LCM = 90 × (x)⇒ x = (GCF × LCM)/90⇒ x = (15 × 450)/90⇒ x = 75Therefore, the other number is 75.


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FAQs ~ above GCF the 75 and 90

What is the GCF the 75 and also 90?

The GCF of 75 and 90 is 15. To calculate the greatest typical factor (GCF) that 75 and also 90, we need to aspect each number (factors of 75 = 1, 3, 5, 15, 25, 75; determinants of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and also choose the greatest variable that precisely divides both 75 and also 90, i.e., 15.

If the GCF the 90 and also 75 is 15, find its LCM.

GCF(90, 75) × LCM(90, 75) = 90 × 75Since the GCF the 90 and also 75 = 15⇒ 15 × LCM(90, 75) = 6750Therefore, LCM = 450☛ Greatest typical Factor Calculator

What is the Relation in between LCM and also GCF that 75, 90?

The adhering to equation have the right to be offered to express the relation in between LCM and GCF of 75 and 90, i.e. GCF × LCM = 75 × 90.

What space the techniques to uncover GCF of 75 and 90?

There room three generally used methods to uncover the GCF of 75 and also 90.

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By Listing typical FactorsBy long DivisionBy element Factorization

How to discover the GCF that 75 and 90 by Long division Method?

To uncover the GCF the 75, 90 making use of long department method, 90 is separated by 75. The corresponding divisor (15) once remainder equates to 0 is taken as GCF.

How to discover the GCF the 75 and 90 by prime Factorization?

To uncover the GCF that 75 and also 90, us will find the element factorization that the offered numbers, i.e. 75 = 3 × 5 × 5; 90 = 2 × 3 × 3 × 5.⇒ because 3, 5 are usual terms in the prime factorization that 75 and 90. Hence, GCF(75, 90) = 3 × 5 = 15☛ What are Prime Numbers?