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GCF of 56 and 35

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

1.	GCF of 56 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 56 and 35?

Answer: GCF of 56 and 35 is 7.

Explanation:

The GCF of two non-zero integers, x(56) and y(35), is the greatest positive integer m(7) that divides both x(56) and y(35) without any remainder.

Methods to Find GCF of 56 and 35

The methods to find the GCF of 56 and 35 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 56 and 35 by Long Division

GCF of 56 and 35 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 56 (larger number) by 35 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (35) by the remainder (21).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the GCF of 56 and 35.

GCF of 56 and 35 by Prime Factorization

Prime factorization of 56 and 35 is (2 × 2 × 2 × 7) and (5 × 7) respectively. As visible, 56 and 35 have only one common prime factor i.e. 7. Hence, the GCF of 56 and 35 is 7.

GCF of 56 and 35 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 = 56 and Y = 35

GCF(56, 35) = GCF(35, 56 mod 35) = GCF(35, 21)
GCF(35, 21) = GCF(21, 35 mod 21) = GCF(21, 14)
GCF(21, 14) = GCF(14, 21 mod 14) = GCF(14, 7)
GCF(14, 7) = GCF(7, 14 mod 7) = GCF(7, 0)
GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 56 and 35 is 7.

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GCF of 56 and 35 Examples

Example 1: For two numbers, GCF = 7 and LCM = 280. If one number is 35, find the other number.

Solution:

Given: GCF (y, 35) = 7 and LCM (y, 35) = 280
∵ GCF × LCM = 35 × (y)
⇒ y = (GCF × LCM)/35
⇒ y = (7 × 280)/35
⇒ y = 56
Therefore, the other number is 56.
Example 2: Find the greatest number that divides 56 and 35 exactly.

Solution:

The greatest number that divides 56 and 35 exactly is their greatest common factor, i.e. GCF of 56 and 35.
⇒ Factors of 56 and 35:
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 35 = 1, 5, 7, 35
Therefore, the GCF of 56 and 35 is 7.
Example 3: The product of two numbers is 1960. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of numbers = 1960
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1960/7
Therefore, the LCM is 280.

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FAQs on GCF of 56 and 35

What is the GCF of 56 and 35?

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

What is the Relation Between LCM and GCF of 56, 35?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 56 and 35, i.e. GCF × LCM = 56 × 35.

What are the Methods to Find GCF of 56 and 35?

There are three commonly used methods to find the GCF of 56 and 35.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the GCF of 35 and 56 is 7, Find its LCM.

GCF(35, 56) × LCM(35, 56) = 35 × 56
Since the GCF of 35 and 56 = 7
⇒ 7 × LCM(35, 56) = 1960
Therefore, LCM = 280
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How to Find the GCF of 56 and 35 by Long Division Method?

To find the GCF of 56, 35 using long division method, 56 is divided by 35. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

How to Find the GCF of 56 and 35 by Prime Factorization?

To find the GCF of 56 and 35, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 35 = 5 × 7.
⇒ Since 7 is the only common prime factor of 56 and 35. Hence, GCF (56, 35) = 7.
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