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

You are watching: What is the gcf of 75 and 90

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

Answer: GCF of 75 and also 90 is 15.

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Explanation:

The GCF of 2 non-zero integers, x(75) and also y(90), is the biggest positive integer m(15) the divides both x(75) and y(90) without any kind of remainder.


The approaches to find the GCF that 75 and also 90 are described below.

Listing typical FactorsPrime administer MethodLong department Method

GCF the 75 and also 90 by Listing typical Factors

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

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

GCF the 75 and 90 by prime Factorization

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

GCF of 75 and 90 by lengthy Division

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GCF the 75 and 90 is the divisor that we obtain when the remainder i do not care 0 after ~ doing long division repeatedly.

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

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

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GCF the 75 and 90 Examples


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

Solution:

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


Example 2: discover the best number that divides 75 and also 90 exactly.

Solution:

The greatest number that divides 75 and 90 exactly is your greatest common factor, i.e. GCF of 75 and also 90.⇒ factors of 75 and 90:

Factors of 75 = 1, 3, 5, 15, 25, 75Factors of 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, uncover the various other number.

Solution:

Given: GCF (x, 90) = 15 and 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 on GCF that 75 and also 90

What is the GCF that 75 and 90?

The GCF the 75 and 90 is 15. To calculate the greatest usual factor (GCF) the 75 and also 90, we require to element each number (factors the 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 variable that specifically divides both 75 and 90, i.e., 15.

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

GCF(90, 75) × LCM(90, 75) = 90 × 75Since the GCF that 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 the 75, 90?

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

What room the approaches to find GCF of 75 and also 90?

There room three commonly used methods to find the GCF that 75 and 90.

See more: How Many Grams Of Spinach In A Cup S Is 100G Spinach? How Much Does 1 Cup Of Spinach Weigh

By Listing common FactorsBy lengthy DivisionBy element Factorization

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

To find the GCF that 75, 90 utilizing long department method, 90 is divided by 75. The equivalent divisor (15) once remainder amounts to 0 is taken as GCF.

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

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