GCF of 15 and 75 is the largest feasible number the divides 15 and also 75 precisely without any kind of remainder. The components of 15 and also 75 space 1, 3, 5, 15 and 1, 3, 5, 15, 25, 75 respectively. There space 3 frequently used techniques to uncover the GCF the 15 and also 75 - lengthy division, Euclidean algorithm, and prime factorization.

You are watching: What is the gcf of 15 and 75

1.GCF that 15 and also 75
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF of 15 and also 75 is 15.

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Explanation:

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


Let's look in ~ the various methods because that finding the GCF the 15 and also 75.

Long division MethodListing typical FactorsPrime factorization Method

GCF of 15 and 75 by lengthy Division

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GCF that 15 and 75 is the divisor that we obtain when the remainder i do not care 0 ~ doing long division repeatedly.

Step 2: because the remainder = 0, the divisor (15) is the GCF the 15 and 75.

The corresponding divisor (15) is the GCF of 15 and 75.

GCF the 15 and 75 by Listing usual Factors

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

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

GCF that 15 and also 75 by prime Factorization

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

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GCF the 15 and 75 Examples


Example 1: find the greatest number the divides 15 and 75 exactly.

Solution:

The best number the divides 15 and also 75 exactly is their greatest usual factor, i.e. GCF the 15 and 75.⇒ components of 15 and also 75:

Factors that 15 = 1, 3, 5, 15Factors that 75 = 1, 3, 5, 15, 25, 75

Therefore, the GCF that 15 and 75 is 15.


Example 2: uncover the GCF of 15 and also 75, if your LCM is 75.

Solution:

∵ LCM × GCF = 15 × 75⇒ GCF(15, 75) = (15 × 75)/75 = 15Therefore, the greatest common factor the 15 and 75 is 15.


Example 3: The product of 2 numbers is 1125. If your GCF is 15, what is your LCM?

Solution:

Given: GCF = 15 and product of number = 1125∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 1125/15Therefore, the LCM is 75.


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FAQs ~ above GCF the 15 and also 75

What is the GCF that 15 and 75?

The GCF that 15 and also 75 is 15. To calculate the greatest typical factor (GCF) that 15 and 75, we require to factor each number (factors that 15 = 1, 3, 5, 15; factors of 75 = 1, 3, 5, 15, 25, 75) and also choose the greatest aspect that precisely divides both 15 and also 75, i.e., 15.

How to discover the GCF that 15 and also 75 by Long division Method?

To discover the GCF that 15, 75 making use of long division method, 75 is separated by 15. The corresponding divisor (15) as soon as remainder amounts to 0 is taken together GCF.

What space the methods to discover GCF of 15 and also 75?

There room three typically used techniques to uncover the GCF that 15 and 75.

By lengthy DivisionBy Euclidean AlgorithmBy element Factorization

How to uncover the GCF the 15 and also 75 by prime Factorization?

To find the GCF that 15 and 75, us will uncover the prime factorization of the offered numbers, i.e. 15 = 3 × 5; 75 = 3 × 5 × 5.⇒ due to the fact that 3, 5 are typical terms in the prime factorization of 15 and also 75. Hence, GCF(15, 75) = 3 × 5 = 15☛ What are Prime Numbers?

What is the Relation in between LCM and also GCF of 15, 75?

The following equation have the right to be supplied to refer the relation between Least usual Multiple and GCF that 15 and also 75, i.e. GCF × LCM = 15 × 75.

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

GCF(75, 15) × LCM(75, 15) = 75 × 15Since the GCF of 75 and also 15 = 15⇒ 15 × LCM(75, 15) = 1125Therefore, LCM = 75☛ Greatest typical Factor Calculator