GCF the 42 and also 60 is the largest feasible number the divides 42 and 60 exactly without any kind of remainder. The factors of 42 and also 60 are 1, 2, 3, 6, 7, 14, 21, 42 and also 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There are 3 frequently used approaches to find the GCF of 42 and 60 - Euclidean algorithm, long division, and also prime factorization.

You are watching: Greatest common factor of 42 and 60

1.GCF that 42 and also 60
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF that 42 and 60 is 6.

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Explanation:

The GCF of 2 non-zero integers, x(42) and y(60), is the best positive essence m(6) the divides both x(42) and also y(60) without any type of remainder.


The techniques to find the GCF the 42 and 60 are explained below.

Long department MethodPrime factorization MethodListing common Factors

GCF the 42 and 60 by long Division

GCF of 42 and 60 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 certainly divide the divisor of step 1 (42) by the remainder (18).Step 3: Repeat this procedure until the remainder = 0.

The equivalent divisor (6) is the GCF that 42 and 60.

GCF that 42 and 60 by prime Factorization

Prime administrate of 42 and 60 is (2 × 3 × 7) and (2 × 2 × 3 × 5) respectively. As visible, 42 and also 60 have common prime factors. Hence, the GCF that 42 and also 60 is 2 × 3 = 6.

GCF the 42 and 60 by Listing typical Factors

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Factors that 42: 1, 2, 3, 6, 7, 14, 21, 42Factors the 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There space 4 common factors the 42 and 60, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 42 and also 60 is 6.

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GCF that 42 and 60 Examples


Example 1: The product of 2 numbers is 2520. If your GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 2520∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 2520/6Therefore, the LCM is 420.


Example 2: For 2 numbers, GCF = 6 and also LCM = 420. If one number is 42, uncover the other number.

Solution:

Given: GCF (x, 42) = 6 and also LCM (x, 42) = 420∵ GCF × LCM = 42 × (x)⇒ x = (GCF × LCM)/42⇒ x = (6 × 420)/42⇒ x = 60Therefore, the other number is 60.


Example 3: uncover the biggest number the divides 42 and 60 exactly.

Solution:

The best number that divides 42 and also 60 exactly is their greatest typical factor, i.e. GCF the 42 and 60.⇒ components of 42 and 60:

Factors that 42 = 1, 2, 3, 6, 7, 14, 21, 42Factors the 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Therefore, the GCF of 42 and also 60 is 6.


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FAQs ~ above GCF the 42 and 60

What is the GCF of 42 and 60?

The GCF of 42 and also 60 is 6. To calculation the GCF that 42 and also 60, we need to factor each number (factors the 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and also choose the greatest variable that specifically divides both 42 and 60, i.e., 6.

If the GCF the 60 and also 42 is 6, find its LCM.

GCF(60, 42) × LCM(60, 42) = 60 × 42Since the GCF that 60 and also 42 = 6⇒ 6 × LCM(60, 42) = 2520Therefore, LCM = 420☛ Greatest usual Factor Calculator

What is the Relation between LCM and GCF the 42, 60?

The complying with equation have the right to be provided to to express the relation between Least usual Multiple and GCF that 42 and 60, i.e. GCF × LCM = 42 × 60.

How to discover the GCF that 42 and 60 through Long division Method?

To find the GCF that 42, 60 utilizing long division method, 60 is divided by 42. The equivalent divisor (6) once remainder equates to 0 is taken together GCF.

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How to uncover the GCF of 42 and also 60 by prime Factorization?

To uncover the GCF of 42 and also 60, us will find the prime factorization of the provided numbers, i.e. 42 = 2 × 3 × 7; 60 = 2 × 2 × 3 × 5.⇒ due to the fact that 2, 3 are common terms in the prime factorization that 42 and 60. Hence, GCF(42, 60) = 2 × 3 = 6☛ prime Number

What space the approaches to uncover GCF the 42 and 60?

There are three typically used techniques to uncover the GCF of 42 and also 60.