GCF of 21 and also 63 is the largest feasible number that divides 21 and 63 exactly without any type of remainder. The determinants of 21 and 63 space 1, 3, 7, 21 and 1, 3, 7, 9, 21, 63 respectively. There space 3 generally used approaches to find the GCF that 21 and also 63 - Euclidean algorithm, prime factorization, and long division.

You are watching: What is the greatest common factor of 21 and 63

1.GCF that 21 and also 63
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF the 21 and also 63 is 21.

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Explanation:

The GCF of two non-zero integers, x(21) and y(63), is the best positive essence m(21) that divides both x(21) and also y(63) without any remainder.


The methods to discover the GCF of 21 and 63 are explained below.

Prime administer MethodLong department MethodListing typical Factors

GCF the 21 and also 63 by prime Factorization

Prime administrate of 21 and 63 is (3 × 7) and (3 × 3 × 7) respectively. Together visible, 21 and 63 have usual prime factors. Hence, the GCF of 21 and also 63 is 3 × 7 = 21.

GCF that 21 and 63 by long Division

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GCF that 21 and also 63 is the divisor that we get when the remainder i do not care 0 after doing long division repeatedly.

Step 2: because the remainder = 0, the divisor (21) is the GCF the 21 and 63.

The matching divisor (21) is the GCF that 21 and also 63.

GCF of 21 and also 63 by Listing common Factors

Factors of 21: 1, 3, 7, 21Factors of 63: 1, 3, 7, 9, 21, 63

There are 4 typical factors the 21 and 63, that are 1, 3, 21, and 7. Therefore, the greatest common factor of 21 and also 63 is 21.

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GCF that 21 and 63 Examples


Example 1: uncover the GCF the 21 and 63, if their LCM is 63.

Solution:

∵ LCM × GCF = 21 × 63⇒ GCF(21, 63) = (21 × 63)/63 = 21Therefore, the greatest typical factor of 21 and 63 is 21.


Example 2: For two numbers, GCF = 21 and also LCM = 63. If one number is 21, find the other number.

Solution:

Given: GCF (x, 21) = 21 and also LCM (x, 21) = 63∵ GCF × LCM = 21 × (x)⇒ x = (GCF × LCM)/21⇒ x = (21 × 63)/21⇒ x = 63Therefore, the other number is 63.


Example 3: The product of 2 numbers is 1323. If your GCF is 21, what is your LCM?

Solution:

Given: GCF = 21 and also product of number = 1323∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 1323/21Therefore, the LCM is 63.


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FAQs top top GCF that 21 and also 63

What is the GCF that 21 and 63?

The GCF of 21 and also 63 is 21. To calculation the greatest typical factor that 21 and also 63, we require to aspect each number (factors of 21 = 1, 3, 7, 21; determinants of 63 = 1, 3, 7, 9, 21, 63) and also choose the greatest variable that exactly divides both 21 and also 63, i.e., 21.

How to find the GCF of 21 and 63 by Long department Method?

To discover the GCF the 21, 63 utilizing long division method, 63 is separated by 21. The matching divisor (21) once remainder equates to 0 is taken together GCF.

What is the Relation between LCM and GCF of 21, 63?

The following equation can be supplied to to express the relation in between Least common Multiple and also GCF of 21 and 63, i.e. GCF × LCM = 21 × 63.

What are the techniques to uncover GCF that 21 and 63?

There room three frequently used techniques to find the GCF of 21 and also 63.

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By long DivisionBy element FactorizationBy Euclidean Algorithm

How to discover the GCF that 21 and also 63 by prime Factorization?

To discover the GCF of 21 and also 63, us will uncover the prime factorization that the offered numbers, i.e. 21 = 3 × 7; 63 = 3 × 3 × 7.⇒ since 3, 7 are common terms in the element factorization that 21 and 63. Hence, GCF(21, 63) = 3 × 7 = 21☛ element Number

If the GCF of 63 and also 21 is 21, discover its LCM.

GCF(63, 21) × LCM(63, 21) = 63 × 21Since the GCF the 63 and 21 = 21⇒ 21 × LCM(63, 21) = 1323Therefore, LCM = 63☛ Greatest usual Factor Calculator