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GCF of 40 and 70

GCF of 40 and 70 is the largest possible number that divides 40 and 70 exactly without any remainder. The factors of 40 and 70 are 1, 2, 4, 5, 8, 10, 20, 40 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There are 3 commonly used methods to find the GCF of 40 and 70 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 40 and 70
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 40 and 70?

Answer: GCF of 40 and 70 is 10.

Explanation:

The GCF of two non-zero integers, x(40) and y(70), is the greatest positive integer m(10) that divides both x(40) and y(70) without any remainder.

Methods to Find GCF of 40 and 70

The methods to find the GCF of 40 and 70 are explained below.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 40 and 70 by Long Division

GCF of 40 and 70 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 70 (larger number) by 40 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (40) by the remainder (30).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the GCF of 40 and 70.

GCF of 40 and 70 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 = 70 and Y = 40

GCF(70, 40) = GCF(40, 70 mod 40) = GCF(40, 30)
GCF(40, 30) = GCF(30, 40 mod 30) = GCF(30, 10)
GCF(30, 10) = GCF(10, 30 mod 10) = GCF(10, 0)
GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 40 and 70 is 10.

GCF of 40 and 70 by Listing Common Factors

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

There are 4 common factors of 40 and 70, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 40 and 70 is 10.

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GCF of 40 and 70 Examples

Example 1: Find the GCF of 40 and 70, if their LCM is 280.

Solution:

∵ LCM × GCF = 40 × 70
⇒ GCF(40, 70) = (40 × 70)/280 = 10
Therefore, the greatest common factor of 40 and 70 is 10.
Example 2: For two numbers, GCF = 10 and LCM = 280. If one number is 70, find the other number.

Solution:

Given: GCF (y, 70) = 10 and LCM (y, 70) = 280
∵ GCF × LCM = 70 × (y)
⇒ y = (GCF × LCM)/70
⇒ y = (10 × 280)/70
⇒ y = 40
Therefore, the other number is 40.
Example 3: Find the greatest number that divides 40 and 70 exactly.

Solution:

The greatest number that divides 40 and 70 exactly is their greatest common factor, i.e. GCF of 40 and 70.
⇒ Factors of 40 and 70:
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
Therefore, the GCF of 40 and 70 is 10.

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FAQs on GCF of 40 and 70

What is the GCF of 40 and 70?

The GCF of 40 and 70 is 10. To calculate the GCF (Greatest Common Factor) of 40 and 70, we need to factor each number (factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40; factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and choose the greatest factor that exactly divides both 40 and 70, i.e., 10.

What is the Relation Between LCM and GCF of 40, 70?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 40 and 70, i.e. GCF × LCM = 40 × 70.

How to Find the GCF of 40 and 70 by Prime Factorization?

To find the GCF of 40 and 70, we will find the prime factorization of the given numbers, i.e. 40 = 2 × 2 × 2 × 5; 70 = 2 × 5 × 7.
⇒ Since 2, 5 are common terms in the prime factorization of 40 and 70. Hence, GCF(40, 70) = 2 × 5 = 10
☛ What is a Prime Number?

What are the Methods to Find GCF of 40 and 70?

There are three commonly used methods to find the GCF of 40 and 70.

By Long Division
By Prime Factorization
By Listing Common Factors

If the GCF of 70 and 40 is 10, Find its LCM.

GCF(70, 40) × LCM(70, 40) = 70 × 40
Since the GCF of 70 and 40 = 10
⇒ 10 × LCM(70, 40) = 2800
Therefore, LCM = 280
☛ Greatest Common Factor Calculator

How to Find the GCF of 40 and 70 by Long Division Method?

To find the GCF of 40, 70 using long division method, 70 is divided by 40. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

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