GCF of 30 and 42 is the largest possible number that divides 30 and also 42 precisely without any type of remainder. The determinants of 30 and also 42 are 1, 2, 3, 5, 6, 10, 15, 30 and also 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to discover the GCF that 30 and 42 - element factorization, lengthy division, and Euclidean algorithm.

You are watching: Greatest common factor of 30 and 42

1.GCF the 30 and also 42
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF the 30 and 42 is 6.

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Explanation:

The GCF of 2 non-zero integers, x(30) and also y(42), is the best positive essence m(6) the divides both x(30) and y(42) without any kind of remainder.


Let's look at the different methods for finding the GCF that 30 and also 42.

Listing common FactorsLong department MethodPrime factorization Method

GCF the 30 and 42 by Listing common Factors

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Factors that 30: 1, 2, 3, 5, 6, 10, 15, 30Factors that 42: 1, 2, 3, 6, 7, 14, 21, 42

There are 4 usual factors of 30 and 42, that room 1, 2, 3, and 6. Therefore, the greatest common factor of 30 and 42 is 6.

GCF the 30 and also 42 by lengthy Division

GCF that 30 and also 42 is the divisor that we acquire when the remainder i do not care 0 after ~ doing long division repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will certainly divide the divisor of action 1 (30) through the remainder (12).Step 3: Repeat this procedure until the remainder = 0.

The corresponding divisor (6) is the GCF the 30 and also 42.

GCF that 30 and also 42 by element Factorization

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Prime administrate of 30 and also 42 is (2 × 3 × 5) and (2 × 3 × 7) respectively. As visible, 30 and also 42 have common prime factors. Hence, the GCF that 30 and 42 is 2 × 3 = 6.

☛ additionally Check:


GCF the 30 and 42 Examples


Example 1: For two numbers, GCF = 6 and also LCM = 210. If one number is 42, find the various other number.

Solution:

Given: GCF (y, 42) = 6 and LCM (y, 42) = 210∵ GCF × LCM = 42 × (y)⇒ y = (GCF × LCM)/42⇒ y = (6 × 210)/42⇒ y = 30Therefore, the various other number is 30.


Example 2: uncover the greatest number that divides 30 and 42 exactly.

Solution:

The biggest number the divides 30 and 42 precisely is your greatest usual factor, i.e. GCF of 30 and also 42.⇒ factors of 30 and also 42:

Factors that 30 = 1, 2, 3, 5, 6, 10, 15, 30Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42

Therefore, the GCF the 30 and also 42 is 6.


Example 3: The product of two numbers is 1260. If your GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 1260∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 1260/6Therefore, the LCM is 210.


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FAQs ~ above GCF the 30 and also 42

What is the GCF that 30 and also 42?

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

How to find the GCF that 30 and 42 through Long department Method?

To find the GCF of 30, 42 making use of long department method, 42 is separated by 30. The matching divisor (6) once remainder equals 0 is taken as GCF.

How to uncover the GCF that 30 and 42 by prime Factorization?

To discover the GCF of 30 and also 42, we will find the element factorization that the given numbers, i.e. 30 = 2 × 3 × 5; 42 = 2 × 3 × 7.⇒ since 2, 3 are usual terms in the prime factorization the 30 and also 42. Hence, GCF(30, 42) = 2 × 3 = 6☛ element Number

If the GCF of 42 and also 30 is 6, discover its LCM.

GCF(42, 30) × LCM(42, 30) = 42 × 30Since the GCF the 42 and also 30 = 6⇒ 6 × LCM(42, 30) = 1260Therefore, LCM = 210☛ Greatest typical Factor Calculator

What is the Relation between LCM and also GCF of 30, 42?

The following equation have the right to be offered to express the relation in between LCM (Least typical Multiple) and also GCF the 30 and also 42, i.e. GCF × LCM = 30 × 42.

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What room the methods to discover GCF that 30 and also 42?

There are three typically used approaches to find the GCF the 30 and 42.