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GCF of 28 and 63

GCF of 28 and 63 is the largest possible number that divides 28 and 63 exactly without any remainder. The factors of 28 and 63 are 1, 2, 4, 7, 14, 28 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 28 and 63 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 28 and 63
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 28 and 63?

Answer: GCF of 28 and 63 is 7.

Explanation:

The GCF of two non-zero integers, x(28) and y(63), is the greatest positive integer m(7) that divides both x(28) and y(63) without any remainder.

Methods to Find GCF of 28 and 63

The methods to find the GCF of 28 and 63 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 28 and 63 by Listing Common Factors

Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 63: 1, 3, 7, 9, 21, 63

There are 2 common factors of 28 and 63, that are 1 and 7. Therefore, the greatest common factor of 28 and 63 is 7.

GCF of 28 and 63 by Long Division

GCF of 28 and 63 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 63 (larger number) by 28 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the GCF of 28 and 63.

GCF of 28 and 63 by Prime Factorization

Prime factorization of 28 and 63 is (2 × 2 × 7) and (3 × 3 × 7) respectively. As visible, 28 and 63 have only one common prime factor i.e. 7. Hence, the GCF of 28 and 63 is 7.

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GCF of 28 and 63 Examples

Example 1: Find the greatest number that divides 28 and 63 exactly.

Solution:

The greatest number that divides 28 and 63 exactly is their greatest common factor, i.e. GCF of 28 and 63.
⇒ Factors of 28 and 63:
- Factors of 28 = 1, 2, 4, 7, 14, 28
- Factors of 63 = 1, 3, 7, 9, 21, 63
Therefore, the GCF of 28 and 63 is 7.
Example 2: For two numbers, GCF = 7 and LCM = 252. If one number is 28, find the other number.

Solution:

Given: GCF (z, 28) = 7 and LCM (z, 28) = 252
∵ GCF × LCM = 28 × (z)
⇒ z = (GCF × LCM)/28
⇒ z = (7 × 252)/28
⇒ z = 63
Therefore, the other number is 63.
Example 3: The product of two numbers is 1764. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of numbers = 1764
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1764/7
Therefore, the LCM is 252.

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FAQs on GCF of 28 and 63

What is the GCF of 28 and 63?

The GCF of 28 and 63 is 7. To calculate the GCF of 28 and 63, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 28 and 63, i.e., 7.

What is the Relation Between LCM and GCF of 28, 63?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 28 and 63, i.e. GCF × LCM = 28 × 63.

If the GCF of 63 and 28 is 7, Find its LCM.

GCF(63, 28) × LCM(63, 28) = 63 × 28
Since the GCF of 63 and 28 = 7
⇒ 7 × LCM(63, 28) = 1764
Therefore, LCM = 252
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How to Find the GCF of 28 and 63 by Long Division Method?

To find the GCF of 28, 63 using long division method, 63 is divided by 28. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

How to Find the GCF of 28 and 63 by Prime Factorization?

To find the GCF of 28 and 63, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 63 = 3 × 3 × 7.
⇒ Since 7 is the only common prime factor of 28 and 63. Hence, GCF (28, 63) = 7.
☛ What is a Prime Number?

What are the Methods to Find GCF of 28 and 63?

There are three commonly used methods to find the GCF of 28 and 63.

By Long Division
By Prime Factorization
By Listing Common Factors

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