GCF that 72 and also 18 is the largest feasible number that divides 72 and also 18 exactly without any type of remainder. The determinants of 72 and 18 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and also 1, 2, 3, 6, 9, 18 respectively. There space 3 frequently used techniques to uncover the GCF that 72 and also 18 - long division, prime factorization, and Euclidean algorithm.

You are watching: Greatest common factor of 72 and 18

1.GCF that 72 and 18
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 72 and also 18 is 18.

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Explanation:

The GCF of 2 non-zero integers, x(72) and y(18), is the greatest positive essence m(18) the divides both x(72) and y(18) without any type of remainder.


Let's look in ~ the different methods because that finding the GCF the 72 and also 18.

Prime administer MethodLong division MethodListing usual Factors

GCF the 72 and also 18 by prime Factorization

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Prime administer of 72 and also 18 is (2 × 2 × 2 × 3 × 3) and also (2 × 3 × 3) respectively. As visible, 72 and 18 have typical prime factors. Hence, the GCF of 72 and also 18 is 2 × 3 × 3 = 18.

GCF the 72 and 18 by lengthy Division

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GCF of 72 and also 18 is the divisor that we gain when the remainder i do not care 0 after ~ doing long department repeatedly.

Step 2: since the remainder = 0, the divisor (18) is the GCF of 72 and 18.

The equivalent divisor (18) is the GCF the 72 and also 18.

GCF of 72 and also 18 through Listing typical Factors

Factors the 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72Factors of 18: 1, 2, 3, 6, 9, 18

There room 6 usual factors of 72 and also 18, that are 1, 2, 3, 6, 9, and 18. Therefore, the greatest usual factor of 72 and also 18 is 18.

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GCF the 72 and also 18 Examples


Example 1: The product of 2 numbers is 1296. If their GCF is 18, what is their LCM?

Solution:

Given: GCF = 18 and product of number = 1296∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 1296/18Therefore, the LCM is 72.


Example 2: uncover the best number the divides 72 and 18 exactly.

Solution:

The greatest number that divides 72 and 18 exactly is their greatest typical factor, i.e. GCF that 72 and 18.⇒ factors of 72 and also 18:

Factors the 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72Factors that 18 = 1, 2, 3, 6, 9, 18

Therefore, the GCF the 72 and also 18 is 18.


Example 3: For two numbers, GCF = 18 and also LCM = 72. If one number is 72, find the other number.

Solution:

Given: GCF (z, 72) = 18 and LCM (z, 72) = 72∵ GCF × LCM = 72 × (z)⇒ z = (GCF × LCM)/72⇒ z = (18 × 72)/72⇒ z = 18Therefore, the other number is 18.


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FAQs ~ above GCF of 72 and also 18

What is the GCF that 72 and also 18?

The GCF of 72 and also 18 is 18. To calculation the greatest usual factor (GCF) that 72 and also 18, we require to factor each number (factors the 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; components of 18 = 1, 2, 3, 6, 9, 18) and choose the greatest element that exactly divides both 72 and 18, i.e., 18.

What is the Relation between LCM and also GCF the 72, 18?

The complying with equation can be offered to refer the relation in between Least common Multiple and GCF of 72 and also 18, i.e. GCF × LCM = 72 × 18.

What space the techniques to discover GCF of 72 and 18?

There are three frequently used methods to find the GCF that 72 and also 18.

By prime FactorizationBy long DivisionBy Euclidean Algorithm

How to discover the GCF the 72 and 18 by element Factorization?

To discover the GCF that 72 and also 18, us will uncover the element factorization the the provided numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 18 = 2 × 3 × 3.⇒ since 2, 3, 3 are common terms in the element factorization of 72 and 18. Hence, GCF(72, 18) = 2 × 3 × 3 = 18☛ element Numbers

If the GCF of 18 and 72 is 18, uncover its LCM.

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GCF(18, 72) × LCM(18, 72) = 18 × 72Since the GCF the 18 and also 72 = 18⇒ 18 × LCM(18, 72) = 1296Therefore, LCM = 72☛ Greatest typical Factor Calculator

How to find the GCF the 72 and 18 through Long department Method?

To uncover the GCF the 72, 18 utilizing long division method, 72 is split by 18. The corresponding divisor (18) when remainder equates to 0 is taken as GCF.