GCF of 24 and 42 is the biggest possible number that divides 24 and also 42 specifically without any type of remainder. The factors of 24 and 42 are 1, 2, 3, 4, 6, 8, 12, 24 and also 1, 2, 3, 6, 7, 14, 21, 42 respectively. Tbelow are 3 commonly offered approaches to discover the GCF of 24 and 42 - Euclidean algorithm, long division, and also prime factorization.

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1.GCF of 24 and 42
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 24 and 42 is 6.

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Explanation:

The GCF of two non-zero integers, x(24) and y(42), is the best positive integer m(6) that divides both x(24) and also y(42) without any type of remainder.


The approaches to uncover the GCF of 24 and 42 are explained listed below.

Long Division MethodListing Typical FactorsPrime Factorization Method

GCF of 24 and also 42 by Long Division

GCF of 24 and also 42 is the divisor that we obtain when the remainder becomes 0 after doing long department continuously.

Tip 2: Because the remainder ≠ 0, we will certainly divide the divisor of action 1 (24) by the remainder (18).Tip 3: Repeat this process till the remainder = 0.

The matching divisor (6) is the GCF of 24 and also 42.

GCF of 24 and also 42 by Listing Usual Factors

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Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

There are 4 common factors of 24 and also 42, that are 1, 2, 3, and also 6. Therefore, the greatest prevalent aspect of 24 and also 42 is 6.

GCF of 24 and also 42 by Prime Factorization

Prime factorization of 24 and 42 is (2 × 2 × 2 × 3) and (2 × 3 × 7) respectively. As visible, 24 and also 42 have actually prevalent prime determinants. Hence, the GCF of 24 and also 42 is 2 × 3 = 6.

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GCF of 24 and 42 Examples


Example 1: Find the GCF of 24 and 42, if their LCM is 168.

Solution:

∵ LCM × GCF = 24 × 42⇒ GCF(24, 42) = (24 × 42)/168 = 6Therefore, the best common factor of 24 and also 42 is 6.


Example 2: For 2 numbers, GCF = 6 and also LCM = 168. If one number is 24, find the various other number.

Solution:

Given: GCF (z, 24) = 6 and also LCM (z, 24) = 168∵ GCF × LCM = 24 × (z)⇒ z = (GCF × LCM)/24⇒ z = (6 × 168)/24⇒ z = 42Therefore, the various other number is 42.


Example 3: The product of 2 numbers is 1008. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 1008∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 1008/6Thus, the LCM is 168.


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FAQs on GCF of 24 and 42

What is the GCF of 24 and 42?

The GCF of 24 and 42 is 6. To calculate the greatest widespread variable (GCF) of 24 and 42, we must aspect each number (components of 24 = 1, 2, 3, 4, 6, 8, 12, 24; determinants of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and pick the best factor that precisely divides both 24 and 42, i.e., 6.

What is the Relation Between LCM and also GCF of 24, 42?

The complying with equation can be offered to express the relation in between Least Usual Multiple (LCM) and also GCF of 24 and also 42, i.e. GCF × LCM = 24 × 42.

What are the Methods to Find GCF of 24 and also 42?

Tbelow are three generally used approaches to discover the GCF of 24 and 42.

By Euclidean AlgorithmBy Prime FactorizationBy Long Division

How to Find the GCF of 24 and 42 by Prime Factorization?

To uncover the GCF of 24 and also 42, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 42 = 2 × 3 × 7.⇒ Due to the fact that 2, 3 are common terms in the prime factorization of 24 and also 42. Hence, GCF(24, 42) = 2 × 3 = 6☛ Prime Numbers

How to Find the GCF of 24 and 42 by Long Division Method?

To find the GCF of 24, 42 utilizing lengthy department technique, 42 is divided by 24. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

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If the GCF of 42 and also 24 is 6, Find its LCM.

GCF(42, 24) × LCM(42, 24) = 42 × 24Since the GCF of 42 and also 24 = 6⇒ 6 × LCM(42, 24) = 1008Thus, LCM = 168☛ Greatest Usual Factor Calculator