GCF that 24 and 42 is the largest feasible number that divides 24 and 42 specifically without any kind of remainder. The determinants of 24 and 42 are 1, 2, 3, 4, 6, 8, 12, 24 and also 1, 2, 3, 6, 7, 14, 21, 42 respectively. There room 3 frequently used methods to find the GCF that 24 and 42 - Euclidean algorithm, lengthy division, and prime factorization.

You are watching: Greatest common factor of 24 and 42

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

Answer: GCF of 24 and also 42 is 6.

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Explanation:

The GCF of 2 non-zero integers, x(24) and y(42), is the greatest positive integer m(6) that divides both x(24) and also y(42) without any kind of remainder.


The methods to uncover the GCF that 24 and also 42 are explained below.

Long division MethodListing usual FactorsPrime administrate Method

GCF that 24 and also 42 by lengthy Division

GCF that 24 and also 42 is the divisor that we get when the remainder i do not care 0 ~ doing long department repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will divide the divisor of action 1 (24) through the remainder (18).Step 3: Repeat this procedure until the remainder = 0.

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

GCF the 24 and 42 through Listing usual Factors

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

There room 4 usual factors that 24 and also 42, that room 1, 2, 3, and also 6. Therefore, the greatest common factor of 24 and 42 is 6.

GCF of 24 and also 42 by element Factorization

Prime administrate of 24 and 42 is (2 × 2 × 2 × 3) and (2 × 3 × 7) respectively. As visible, 24 and 42 have usual prime factors. Hence, the GCF of 24 and also 42 is 2 × 3 = 6.

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GCF of 24 and 42 Examples


Example 1: discover the GCF the 24 and 42, if your LCM is 168.

Solution:

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


Example 2: For two numbers, GCF = 6 and LCM = 168. If one number is 24, uncover 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 your GCF is 6, what is their LCM?

Solution:

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


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FAQs top top GCF that 24 and also 42

What is the GCF that 24 and 42?

The GCF the 24 and 42 is 6. To calculation the greatest common factor (GCF) the 24 and also 42, we require to factor each number (factors the 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and also choose the greatest element that exactly divides both 24 and also 42, i.e., 6.

What is the Relation between LCM and GCF that 24, 42?

The adhering to equation have the right to be provided to to express the relation between Least typical Multiple (LCM) and also GCF the 24 and 42, i.e. GCF × LCM = 24 × 42.

What are the methods to uncover GCF of 24 and also 42?

There space three typically used methods to uncover the GCF the 24 and 42.

By Euclidean AlgorithmBy prime FactorizationBy long Division

How to find the GCF of 24 and also 42 by element Factorization?

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

How to find the GCF of 24 and 42 by Long division Method?

To discover the GCF the 24, 42 making use of long department method, 42 is divided by 24. The corresponding divisor (6) once remainder equates to 0 is taken together GCF.

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If the GCF the 42 and 24 is 6, discover its LCM.

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