GCF of 10 and 30 is the largest possible number that divides 10 and also 30 precisely without any type of remainder. The determinants of 10 and also 30 are 1, 2, 5, 10 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. Tbelow are 3 typically provided methods to discover the GCF of 10 and 30 - long department, prime factorization, and also Euclidean algorithm.

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1.GCF of 10 and also 30
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 10 and 30 is 10.

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Explanation:

The GCF of 2 non-zero integers, x(10) and also y(30), is the best positive integer m(10) that divides both x(10) and y(30) without any kind of remainder.


The techniques to find the GCF of 10 and 30 are defined listed below.

Prime Factorization MethodUsing Euclid's AlgorithmLong Division Method

GCF of 10 and 30 by Prime Factorization

Prime factorization of 10 and 30 is (2 × 5) and also (2 × 3 × 5) respectively. As visible, 10 and 30 have actually prevalent prime factors. Hence, the GCF of 10 and 30 is 2 × 5 = 10.

GCF of 10 and also 30 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)where X > Y and mod is the modulo operator.

Here X = 30 and Y = 10

GCF(30, 10) = GCF(10, 30 mod 10) = GCF(10, 0)GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, wbelow X ≠ 0)

Because of this, the worth of GCF of 10 and also 30 is 10.

GCF of 10 and 30 by Long Division

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GCF of 10 and 30 is the divisor that we obtain as soon as the remainder becomes 0 after doing long department repetitively.

Step 2: Because the remainder = 0, the divisor (10) is the GCF of 10 and also 30.

The matching divisor (10) is the GCF of 10 and 30.

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GCF of 10 and 30 Examples


Example 1: Find the GCF of 10 and also 30, if their LCM is 30.

Solution:

∵ LCM × GCF = 10 × 30⇒ GCF(10, 30) = (10 × 30)/30 = 10Because of this, the greatest common variable of 10 and 30 is 10.


Example 2: The product of 2 numbers is 300. If their GCF is 10, what is their LCM?

Solution:

Given: GCF = 10 and product of numbers = 300∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 300/10Because of this, the LCM is 30.


Example 3: Find the best number that divides 10 and 30 precisely.

Solution:

The greatest number that divides 10 and 30 specifically is their biggest common element, i.e. GCF of 10 and also 30.⇒ Factors of 10 and 30:

Factors of 10 = 1, 2, 5, 10Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30

Therefore, the GCF of 10 and also 30 is 10.


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FAQs on GCF of 10 and also 30

What is the GCF of 10 and also 30?

The GCF of 10 and 30 is 10. To calculate the greatest widespread variable (GCF) of 10 and 30, we have to factor each number (determinants of 10 = 1, 2, 5, 10; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and also pick the biggest factor that exactly divides both 10 and 30, i.e., 10.

How to Find the GCF of 10 and also 30 by Long Division Method?

To uncover the GCF of 10, 30 utilizing long department method, 30 is separated by 10. The equivalent divisor (10) as soon as remainder equates to 0 is taken as GCF.

If the GCF of 30 and 10 is 10, Find its LCM.

GCF(30, 10) × LCM(30, 10) = 30 × 10Since the GCF of 30 and also 10 = 10⇒ 10 × LCM(30, 10) = 300As such, LCM = 30☛ Greatest Usual Factor Calculator

What is the Relation Between LCM and also GCF of 10, 30?

The following equation have the right to be provided to expush the relation in between Leastern Typical Multiple (LCM) and also GCF of 10 and 30, i.e. GCF × LCM = 10 × 30.

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What are the Methods to Find GCF of 10 and also 30?

There are 3 generally offered methods to discover the GCF of 10 and 30.

By Long DivisionBy Euclidean AlgorithmBy Prime Factorization

How to Find the GCF of 10 and 30 by Prime Factorization?

To find the GCF of 10 and also 30, we will uncover the prime factorization of the offered numbers, i.e. 10 = 2 × 5; 30 = 2 × 3 × 5.⇒ Since 2, 5 are common terms in the prime factorization of 10 and also 30. Hence, GCF(10, 30) = 2 × 5 = 10☛ Prime Number