GCF of 12 and also 60 is the largest possible number that divides 12 and 60 precisely without any kind of remainder. The determinants of 12 and 60 space 1, 2, 3, 4, 6, 12 and also 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There space 3 typically used methods to find the GCF that 12 and also 60 - long division, element factorization, and also Euclidean algorithm.

You are watching: What is the gcf of 12 and 60

1.GCF of 12 and 60
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF that 12 and 60 is 12.

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Explanation:

The GCF of 2 non-zero integers, x(12) and also y(60), is the best positive integer m(12) that divides both x(12) and y(60) without any type of remainder.


The techniques to find the GCF the 12 and also 60 are described below.

Using Euclid's AlgorithmLong department MethodListing common Factors

GCF the 12 and 60 through Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode Y)where X > Y and also mod is the modulo operator.

Here X = 60 and also Y = 12

GCF(60, 12) = GCF(12, 60 mode 12) = GCF(12, 0)GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the worth of GCF the 12 and 60 is 12.

GCF of 12 and also 60 by lengthy Division

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GCF the 12 and also 60 is the divisor the we gain when the remainder i do not care 0 ~ doing long division repeatedly.

Step 2: since the remainder = 0, the divisor (12) is the GCF that 12 and 60.

The matching divisor (12) is the GCF that 12 and also 60.

GCF of 12 and also 60 by Listing typical Factors

Factors of 12: 1, 2, 3, 4, 6, 12Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There are 6 typical factors of 12 and also 60, that room 1, 2, 3, 4, 6, and 12. Therefore, the greatest usual factor the 12 and also 60 is 12.

☛ likewise Check:


GCF of 12 and also 60 Examples


Example 1: The product of 2 numbers is 720. If your GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and also product of number = 720∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 720/12Therefore, the LCM is 60.


Example 2: uncover the biggest number the divides 12 and 60 exactly.

Solution:

The greatest number the divides 12 and 60 precisely is your greatest common factor, i.e. GCF of 12 and also 60.⇒ components of 12 and 60:

Factors of 12 = 1, 2, 3, 4, 6, 12Factors the 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Therefore, the GCF that 12 and 60 is 12.


Example 3: For 2 numbers, GCF = 12 and LCM = 60. If one number is 60, find the various other number.

Solution:

Given: GCF (y, 60) = 12 and also LCM (y, 60) = 60∵ GCF × LCM = 60 × (y)⇒ y = (GCF × LCM)/60⇒ y = (12 × 60)/60⇒ y = 12Therefore, the other number is 12.


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FAQs on GCF of 12 and also 60

What is the GCF of 12 and also 60?

The GCF the 12 and also 60 is 12. To calculation the GCF the 12 and also 60, we require to element each number (factors of 12 = 1, 2, 3, 4, 6, 12; determinants of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest element that exactly divides both 12 and 60, i.e., 12.

How to discover the GCF that 12 and 60 by element Factorization?

To discover the GCF the 12 and 60, us will discover the prime factorization the the offered numbers, i.e. 12 = 2 × 2 × 3; 60 = 2 × 2 × 3 × 5.⇒ because 2, 2, 3 are usual terms in the prime factorization the 12 and also 60. Hence, GCF(12, 60) = 2 × 2 × 3 = 12☛ prime Numbers

What is the Relation in between LCM and also GCF the 12, 60?

The adhering to equation have the right to be used to refer the relation between Least typical Multiple (LCM) and GCF that 12 and 60, i.e. GCF × LCM = 12 × 60.

What are the techniques to uncover GCF that 12 and 60?

There room three typically used techniques to discover the GCF that 12 and also 60.

By prime FactorizationBy long DivisionBy Euclidean Algorithm

If the GCF that 60 and also 12 is 12, discover its LCM.

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GCF(60, 12) × LCM(60, 12) = 60 × 12Since the GCF the 60 and also 12 = 12⇒ 12 × LCM(60, 12) = 720Therefore, LCM = 60☛ GCF Calculator

How to uncover the GCF of 12 and 60 through Long division Method?

To discover the GCF of 12, 60 utilizing long department method, 60 is separated by 12. The corresponding divisor (12) when remainder amounts to 0 is taken together GCF.