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GCF of 56 and 70

GCF of 56 and 70 is the largest possible number that divides 56 and 70 exactly without any remainder. The factors of 56 and 70 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There are 3 commonly used methods to find the GCF of 56 and 70 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 56 and 70
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 56 and 70?

Answer: GCF of 56 and 70 is 14.

Explanation:

The GCF of two non-zero integers, x(56) and y(70), is the greatest positive integer m(14) that divides both x(56) and y(70) without any remainder.

Methods to Find GCF of 56 and 70

Let's look at the different methods for finding the GCF of 56 and 70.

Using Euclid's Algorithm
Prime Factorization Method
Listing Common Factors

GCF of 56 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 = 56

GCF(70, 56) = GCF(56, 70 mod 56) = GCF(56, 14)
GCF(56, 14) = GCF(14, 56 mod 14) = GCF(14, 0)
GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 56 and 70 is 14.

GCF of 56 and 70 by Prime Factorization

Prime factorization of 56 and 70 is (2 × 2 × 2 × 7) and (2 × 5 × 7) respectively. As visible, 56 and 70 have common prime factors. Hence, the GCF of 56 and 70 is 2 × 7 = 14.

GCF of 56 and 70 by Listing Common Factors

Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

There are 4 common factors of 56 and 70, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 56 and 70 is 14.

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GCF of 56 and 70 Examples

Example 1: Find the GCF of 56 and 70, if their LCM is 280.

Solution:

∵ LCM × GCF = 56 × 70
⇒ GCF(56, 70) = (56 × 70)/280 = 14
Therefore, the greatest common factor of 56 and 70 is 14.
Example 2: The product of two numbers is 3920. If their GCF is 14, what is their LCM?

Solution:

Given: GCF = 14 and product of numbers = 3920
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3920/14
Therefore, the LCM is 280.
Example 3: Find the greatest number that divides 56 and 70 exactly.

Solution:

The greatest number that divides 56 and 70 exactly is their greatest common factor, i.e. GCF of 56 and 70.
⇒ Factors of 56 and 70:
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
Therefore, the GCF of 56 and 70 is 14.

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FAQs on GCF of 56 and 70

What is the GCF of 56 and 70?

The GCF of 56 and 70 is 14. To calculate the greatest common factor of 56 and 70, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and choose the greatest factor that exactly divides both 56 and 70, i.e., 14.

What is the Relation Between LCM and GCF of 56, 70?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 56 and 70, i.e. GCF × LCM = 56 × 70.

How to Find the GCF of 56 and 70 by Long Division Method?

To find the GCF of 56, 70 using long division method, 70 is divided by 56. The corresponding divisor (14) when remainder equals 0 is taken as GCF.

If the GCF of 70 and 56 is 14, Find its LCM.

GCF(70, 56) × LCM(70, 56) = 70 × 56
Since the GCF of 70 and 56 = 14
⇒ 14 × LCM(70, 56) = 3920
Therefore, LCM = 280
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How to Find the GCF of 56 and 70 by Prime Factorization?

To find the GCF of 56 and 70, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 70 = 2 × 5 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 56 and 70. Hence, GCF(56, 70) = 2 × 7 = 14
☛ Prime Numbers

What are the Methods to Find GCF of 56 and 70?

There are three commonly used methods to find the GCF of 56 and 70.

By Long Division
By Prime Factorization
By Listing Common Factors

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