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GCF of 45 and 63

GCF of 45 and 63 is the largest possible number that divides 45 and 63 exactly without any remainder. The factors of 45 and 63 are 1, 3, 5, 9, 15, 45 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 45 and 63 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 45 and 63
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 45 and 63?

Answer: GCF of 45 and 63 is 9.

Explanation:

The GCF of two non-zero integers, x(45) and y(63), is the greatest positive integer m(9) that divides both x(45) and y(63) without any remainder.

Methods to Find GCF of 45 and 63

The methods to find the GCF of 45 and 63 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 45 and 63 by Long Division

GCF of 45 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 45 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (45) by the remainder (18).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 45 and 63.

GCF of 45 and 63 by Prime Factorization

Prime factorization of 45 and 63 is (3 × 3 × 5) and (3 × 3 × 7) respectively. As visible, 45 and 63 have common prime factors. Hence, the GCF of 45 and 63 is 3 × 3 = 9.

GCF of 45 and 63 by Listing Common Factors

Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 63: 1, 3, 7, 9, 21, 63

There are 3 common factors of 45 and 63, that are 1, 3, and 9. Therefore, the greatest common factor of 45 and 63 is 9.

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GCF of 45 and 63 Examples

Example 1: Find the GCF of 45 and 63, if their LCM is 315.

Solution:

∵ LCM × GCF = 45 × 63
⇒ GCF(45, 63) = (45 × 63)/315 = 9
Therefore, the greatest common factor of 45 and 63 is 9.
Example 2: Find the greatest number that divides 45 and 63 exactly.

Solution:

The greatest number that divides 45 and 63 exactly is their greatest common factor, i.e. GCF of 45 and 63.
⇒ Factors of 45 and 63:
- Factors of 45 = 1, 3, 5, 9, 15, 45
- Factors of 63 = 1, 3, 7, 9, 21, 63
Therefore, the GCF of 45 and 63 is 9.
Example 3: The product of two numbers is 2835. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 2835
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2835/9
Therefore, the LCM is 315.

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FAQs on GCF of 45 and 63

What is the GCF of 45 and 63?

The GCF of 45 and 63 is 9. To calculate the greatest common factor of 45 and 63, we need to factor each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 45 and 63, i.e., 9.

How to Find the GCF of 45 and 63 by Prime Factorization?

To find the GCF of 45 and 63, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 63 = 3 × 3 × 7.
⇒ Since 3, 3 are common terms in the prime factorization of 45 and 63. Hence, GCF(45, 63) = 3 × 3 = 9
☛ Prime Number

How to Find the GCF of 45 and 63 by Long Division Method?

To find the GCF of 45, 63 using long division method, 63 is divided by 45. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

If the GCF of 63 and 45 is 9, Find its LCM.

GCF(63, 45) × LCM(63, 45) = 63 × 45
Since the GCF of 63 and 45 = 9
⇒ 9 × LCM(63, 45) = 2835
Therefore, LCM = 315
☛ GCF Calculator

What is the Relation Between LCM and GCF of 45, 63?

The following equation can be used to express the relation between Least Common Multiple and GCF of 45 and 63, i.e. GCF × LCM = 45 × 63.

What are the Methods to Find GCF of 45 and 63?

There are three commonly used methods to find the GCF of 45 and 63.

By Long Division
By Listing Common Factors
By Prime Factorization

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