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GCF of 40 and 63

GCF of 40 and 63 is the largest possible number that divides 40 and 63 exactly without any remainder. The factors of 40 and 63 are 1, 2, 4, 5, 8, 10, 20, 40 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 40 and 63 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 40 and 63
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 40 and 63?

Answer: GCF of 40 and 63 is 1.

Explanation:

The GCF of two non-zero integers, x(40) and y(63), is the greatest positive integer m(1) that divides both x(40) and y(63) without any remainder.

Methods to Find GCF of 40 and 63

Let's look at the different methods for finding the GCF of 40 and 63.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 40 and 63 by Prime Factorization

Prime factorization of 40 and 63 is (2 × 2 × 2 × 5) and (3 × 3 × 7) respectively. As visible, there are no common prime factors between 40 and 63, i.e. they are co-prime. Hence, the GCF of 40 and 63 will be 1.

GCF of 40 and 63 by Listing Common Factors

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 63: 1, 3, 7, 9, 21, 63

Since, 1 is the only common factor between 40 and 63. The Greatest Common Factor of 40 and 63 is 1.

GCF of 40 and 63 by Long Division

GCF of 40 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 40 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (40) by the remainder (23).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 40 and 63.

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GCF of 40 and 63 Examples

Example 1: Find the GCF of 40 and 63, if their LCM is 2520.

Solution:

∵ LCM × GCF = 40 × 63
⇒ GCF(40, 63) = (40 × 63)/2520 = 1
Therefore, the greatest common factor of 40 and 63 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 2520. If one number is 40, find the other number.

Solution:

Given: GCF (x, 40) = 1 and LCM (x, 40) = 2520
∵ GCF × LCM = 40 × (x)
⇒ x = (GCF × LCM)/40
⇒ x = (1 × 2520)/40
⇒ x = 63
Therefore, the other number is 63.
Example 3: Find the greatest number that divides 40 and 63 exactly.

Solution:

The greatest number that divides 40 and 63 exactly is their greatest common factor, i.e. GCF of 40 and 63.
⇒ Factors of 40 and 63:
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 63 = 1, 3, 7, 9, 21, 63
Therefore, the GCF of 40 and 63 is 1.

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FAQs on GCF of 40 and 63

What is the GCF of 40 and 63?

The GCF of 40 and 63 is 1. To calculate the greatest common factor of 40 and 63, we need to factor each number (factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 40 and 63, i.e., 1.

What is the Relation Between LCM and GCF of 40, 63?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 40 and 63, i.e. GCF × LCM = 40 × 63.

How to Find the GCF of 40 and 63 by Prime Factorization?

To find the GCF of 40 and 63, we will find the prime factorization of the given numbers, i.e. 40 = 2 × 2 × 2 × 5; 63 = 3 × 3 × 7.
⇒ There is no common prime factor for 40 and 63. Hence, GCF (40, 63) = 1.
☛ What are Prime Numbers?

What are the Methods to Find GCF of 40 and 63?

There are three commonly used methods to find the GCF of 40 and 63.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the GCF of 63 and 40 is 1, Find its LCM.

GCF(63, 40) × LCM(63, 40) = 63 × 40
Since the GCF of 63 and 40 = 1
⇒ 1 × LCM(63, 40) = 2520
Therefore, LCM = 2520
☛ Greatest Common Factor Calculator

How to Find the GCF of 40 and 63 by Long Division Method?

To find the GCF of 40, 63 using long division method, 63 is divided by 40. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

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