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GCF of 10 and 40

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

1.	GCF of 10 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 40?

Answer: GCF of 10 and 40 is 10.

Explanation:

The GCF of two non-zero integers, x(10) and y(40), is the greatest positive integer m(10) that divides both x(10) and y(40) without any remainder.

Methods to Find GCF of 10 and 40

The methods to find the GCF of 10 and 40 are explained below.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

GCF of 10 and 40 by Listing Common Factors

Factors of 10: 1, 2, 5, 10
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

There are 4 common factors of 10 and 40, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 10 and 40 is 10.

GCF of 10 and 40 by Long Division

GCF of 10 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 40 (larger number) by 10 (smaller number).
Step 2: Since the remainder = 0, the divisor (10) is the GCF of 10 and 40.

The corresponding divisor (10) is the GCF of 10 and 40.

GCF of 10 and 40 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 40 and Y = 10

GCF(40, 10) = GCF(10, 40 mod 10) = GCF(10, 0)
GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 10 and 40 is 10.

☛ Also Check:

GCF of 10 and 40 Examples

Example 1: For two numbers, GCF = 10 and LCM = 40. If one number is 40, find the other number.

Solution:

Given: GCF (z, 40) = 10 and LCM (z, 40) = 40
∵ GCF × LCM = 40 × (z)
⇒ z = (GCF × LCM)/40
⇒ z = (10 × 40)/40
⇒ z = 10
Therefore, the other number is 10.
Example 2: Find the GCF of 10 and 40, if their LCM is 40.

Solution:

∵ LCM × GCF = 10 × 40
⇒ GCF(10, 40) = (10 × 40)/40 = 10
Therefore, the greatest common factor of 10 and 40 is 10.
Example 3: Find the greatest number that divides 10 and 40 exactly.

Solution:

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

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FAQs on GCF of 10 and 40

What is the GCF of 10 and 40?

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

How to Find the GCF of 10 and 40 by Long Division Method?

To find the GCF of 10, 40 using long division method, 40 is divided by 10. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

How to Find the GCF of 10 and 40 by Prime Factorization?

To find the GCF of 10 and 40, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 10 and 40. Hence, GCF(10, 40) = 2 × 5 = 10
☛ What are Prime Numbers?

What are the Methods to Find GCF of 10 and 40?

There are three commonly used methods to find the GCF of 10 and 40.

By Long Division
By Listing Common Factors
By Prime Factorization

If the GCF of 40 and 10 is 10, Find its LCM.

GCF(40, 10) × LCM(40, 10) = 40 × 10
Since the GCF of 40 and 10 = 10
⇒ 10 × LCM(40, 10) = 400
Therefore, LCM = 40
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What is the Relation Between LCM and GCF of 10, 40?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 10 and 40, i.e. GCF × LCM = 10 × 40.

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