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

You are watching: What is the gcf of 30 and 42

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

Answer: GCF the 30 and also 42 is 6.

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Explanation:

The GCF of 2 non-zero integers, x(30) and y(42), is the greatest positive integer m(6) that divides both x(30) and y(42) without any remainder.


Let's look in ~ the different methods for finding the GCF of 30 and 42.

Listing usual FactorsLong department MethodPrime administer Method

GCF of 30 and 42 through Listing typical Factors

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

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

GCF of 30 and 42 by long Division

GCF the 30 and 42 is the divisor that we obtain when the remainder i do not care 0 after doing long department repeatedly.

Step 2: since the remainder ≠ 0, we will certainly divide the divisor of step 1 (30) by the remainder (12).Step 3: Repeat this procedure until the remainder = 0.

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

GCF the 30 and 42 by prime Factorization

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

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GCF that 30 and 42 Examples


Example 1: For 2 numbers, GCF = 6 and also LCM = 210. If one number is 42, uncover the other number.

Solution:

Given: GCF (y, 42) = 6 and also 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: find the biggest number the divides 30 and also 42 exactly.

Solution:

The biggest number that divides 30 and 42 exactly is their greatest usual factor, i.e. GCF that 30 and 42.⇒ components of 30 and also 42:

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

Therefore, the GCF of 30 and 42 is 6.


Example 3: The product of two numbers is 1260. If your GCF is 6, what is your 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 of 30 and also 42

What is the GCF of 30 and also 42?

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

How to find the GCF of 30 and also 42 through Long division Method?

To find the GCF the 30, 42 using long division method, 42 is divided by 30. The matching divisor (6) when remainder equals 0 is taken together GCF.

How to find the GCF the 30 and 42 by element Factorization?

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

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

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

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

The complying with equation have the right to be supplied to to express the relation between LCM (Least typical Multiple) and also GCF of 30 and 42, i.e. GCF × LCM = 30 × 42.

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What space the methods to discover GCF the 30 and also 42?

There are three commonly used approaches to uncover the GCF the 30 and 42.