GCF that 21 and 63 is the largest possible number the divides 21 and also 63 precisely without any kind of remainder. The factors of 21 and 63 room 1, 3, 7, 21 and also 1, 3, 7, 9, 21, 63 respectively. There are 3 frequently used approaches to uncover the GCF the 21 and 63 - Euclidean algorithm, element factorization, and also long division.

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

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

Answer: GCF of 21 and also 63 is 21.

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Explanation:

The GCF of 2 non-zero integers, x(21) and y(63), is the greatest positive creature m(21) that divides both x(21) and y(63) without any remainder.


The approaches to find the GCF that 21 and 63 are explained below.

Prime administer MethodLong division MethodListing typical Factors

GCF the 21 and also 63 by element Factorization

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

GCF that 21 and 63 by lengthy Division

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GCF of 21 and 63 is the divisor that we gain when the remainder becomes 0 after ~ doing long department repeatedly.

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

The corresponding divisor (21) is the GCF of 21 and 63.

GCF of 21 and 63 by Listing typical Factors

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

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

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GCF the 21 and 63 Examples


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

Solution:

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


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


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

Solution:

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


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FAQs on GCF that 21 and also 63

What is the GCF the 21 and also 63?

The GCF that 21 and also 63 is 21. To calculate the greatest usual factor the 21 and 63, we require to factor each number (factors that 21 = 1, 3, 7, 21; components of 63 = 1, 3, 7, 9, 21, 63) and also choose the greatest factor that specifically divides both 21 and 63, i.e., 21.

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

To discover the GCF that 21, 63 utilizing long division method, 63 is divided by 21. The corresponding divisor (21) as soon as remainder equates to 0 is taken as GCF.

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

The complying with equation have the right to be offered to express the relation between Least common Multiple and GCF that 21 and also 63, i.e. GCF × LCM = 21 × 63.

What space the approaches to discover GCF the 21 and also 63?

There room three typically used methods to discover the GCF that 21 and also 63.

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By lengthy DivisionBy element FactorizationBy Euclidean Algorithm

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

To find the GCF the 21 and 63, we will uncover the element factorization of the given numbers, i.e. 21 = 3 × 7; 63 = 3 × 3 × 7.⇒ since 3, 7 are usual terms in the element factorization that 21 and 63. Hence, GCF(21, 63) = 3 × 7 = 21☛ prime Number

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

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