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

You are watching: What is the greatest common factor of 90 and 75

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

Answer: GCF the 75 and also 90 is 15.

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Explanation:

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


The techniques to uncover the GCF that 75 and also 90 are explained below.

Listing usual FactorsPrime administer MethodLong division Method

GCF of 75 and also 90 by Listing typical Factors

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

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

GCF that 75 and also 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 common prime factors. Hence, the GCF of 75 and also 90 is 3 × 5 = 15.

GCF that 75 and 90 by long Division

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

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

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

☛ likewise Check:


GCF that 75 and 90 Examples


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

Solution:

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


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

Solution:

The best number the divides 75 and 90 exactly is their greatest typical factor, i.e. GCF of 75 and 90.⇒ components of 75 and 90:

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

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


Example 3: For 2 numbers, GCF = 15 and also LCM = 450. If one number is 90, find the various 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 various other number is 75.


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FAQs top top GCF the 75 and also 90

What is the GCF of 75 and 90?

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

If the GCF that 90 and also 75 is 15, uncover 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 of 75, 90?

The following equation deserve to be used to express the relation in between LCM and also GCF the 75 and 90, i.e. GCF × LCM = 75 × 90.

What room the methods to uncover GCF the 75 and also 90?

There are three frequently used techniques to find the GCF of 75 and 90.

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By Listing typical FactorsBy long DivisionBy element Factorization

How to uncover the GCF that 75 and 90 by Long department Method?

To uncover the GCF that 75, 90 using long division method, 90 is split by 75. The equivalent divisor (15) when remainder equals 0 is taken together GCF.

How to uncover the GCF the 75 and 90 by element Factorization?

To discover the GCF of 75 and 90, we will discover the element factorization of the offered numbers, i.e. 75 = 3 × 5 × 5; 90 = 2 × 3 × 3 × 5.⇒ since 3, 5 are usual terms in the element factorization that 75 and also 90. Hence, GCF(75, 90) = 3 × 5 = 15☛ What space Prime Numbers?