GCF the 30 and 42 is the largest feasible number that 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 also 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 frequently used techniques to uncover the GCF the 30 and 42 - prime factorization, lengthy division, and Euclidean algorithm.

You are watching: What is the greatest common factor of 30 and 42

1.GCF of 30 and 42
2.List of 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 y(42), is the biggest positive essence m(6) the divides both x(30) and also y(42) without any type of remainder.


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

Listing common FactorsLong division MethodPrime administer Method

GCF the 30 and also 42 by Listing typical Factors

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

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

GCF that 30 and also 42 by long Division

GCF the 30 and 42 is the divisor the we acquire when the remainder becomes 0 ~ doing long division repeatedly.

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

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

GCF of 30 and 42 by prime Factorization

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

☛ also Check:


GCF the 30 and 42 Examples


Example 1: For 2 numbers, GCF = 6 and also LCM = 210. If one number is 42, uncover 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 other number is 30.


Example 2: discover the greatest number the divides 30 and also 42 exactly.

Solution:

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

Factors the 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 also 42 is 6.


Example 3: The product of 2 numbers is 1260. If their GCF is 6, what is their LCM?

Solution:

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


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FAQs top top GCF the 30 and also 42

What is the GCF the 30 and also 42?

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

How to find the GCF that 30 and 42 by Long division Method?

To find the GCF that 30, 42 making use of long division method, 42 is divided by 30. The matching divisor (6) as soon as remainder amounts to 0 is taken together GCF.

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

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

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

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

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

The adhering to equation deserve to be offered 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 room the methods to find GCF of 30 and 42?

There room three commonly used approaches to find the GCF that 30 and 42.