GCF that 75 and 90 is the largest possible number the divides 75 and also 90 specifically without any type of remainder. The components of 75 and 90 are 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 - lengthy division, Euclidean algorithm, and also prime factorization.

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

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

Answer: GCF the 75 and 90 is 15.

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Explanation:

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


The techniques to find the GCF of 75 and also 90 are defined below.

Listing usual FactorsPrime factorization MethodLong department Method

GCF of 75 and also 90 through Listing common Factors

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

There room 4 common 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 administrate of 75 and 90 is (3 × 5 × 5) and also (2 × 3 × 3 × 5) respectively. As visible, 75 and 90 have typical prime factors. Hence, the GCF of 75 and also 90 is 3 × 5 = 15.

GCF of 75 and also 90 by lengthy Division

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

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

The equivalent divisor (15) is the GCF that 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 their LCM?

Solution:

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


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

Solution:

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

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

Therefore, the GCF that 75 and 90 is 15.


Example 3: For 2 numbers, GCF = 15 and also LCM = 450. If one number is 90, uncover the 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 top top GCF of 75 and 90

What is the GCF that 75 and 90?

The GCF of 75 and 90 is 15. To calculation the greatest common factor (GCF) the 75 and 90, we require 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 choose the greatest factor that specifically divides both 75 and also 90, i.e., 15.

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

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

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

The complying with equation have the right to be supplied to refer the relation between LCM and also GCF the 75 and also 90, i.e. GCF × LCM = 75 × 90.

What room the approaches to uncover GCF that 75 and 90?

There room three frequently used techniques to uncover the GCF that 75 and 90.

See more: Which Geometric Object Is The Shortest Path Between Two Points

By Listing typical FactorsBy lengthy DivisionBy prime Factorization

How to find the GCF the 75 and also 90 through Long division Method?

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

How to find the GCF that 75 and 90 by prime Factorization?

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