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GCF of 55 and 75

GCF of 55 and 75 is the largest possible number that divides 55 and 75 exactly without any remainder. The factors of 55 and 75 are 1, 5, 11, 55 and 1, 3, 5, 15, 25, 75 respectively. There are 3 commonly used methods to find the GCF of 55 and 75 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 55 and 75
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 55 and 75?

Answer: GCF of 55 and 75 is 5.

Explanation:

The GCF of two non-zero integers, x(55) and y(75), is the greatest positive integer m(5) that divides both x(55) and y(75) without any remainder.

Methods to Find GCF of 55 and 75

The methods to find the GCF of 55 and 75 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 55 and 75 by Prime Factorization

Prime factorization of 55 and 75 is (5 × 11) and (3 × 5 × 5) respectively. As visible, 55 and 75 have only one common prime factor i.e. 5. Hence, the GCF of 55 and 75 is 5.

GCF of 55 and 75 by Long Division

GCF of 55 and 75 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 75 (larger number) by 55 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (55) by the remainder (20).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 55 and 75.

GCF of 55 and 75 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 = 75 and Y = 55

GCF(75, 55) = GCF(55, 75 mod 55) = GCF(55, 20)
GCF(55, 20) = GCF(20, 55 mod 20) = GCF(20, 15)
GCF(20, 15) = GCF(15, 20 mod 15) = GCF(15, 5)
GCF(15, 5) = GCF(5, 15 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 55 and 75 is 5.

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GCF of 55 and 75 Examples

Example 1: Find the GCF of 55 and 75, if their LCM is 825.

Solution:

∵ LCM × GCF = 55 × 75
⇒ GCF(55, 75) = (55 × 75)/825 = 5
Therefore, the greatest common factor of 55 and 75 is 5.
Example 2: Find the greatest number that divides 55 and 75 exactly.

Solution:

The greatest number that divides 55 and 75 exactly is their greatest common factor, i.e. GCF of 55 and 75.
⇒ Factors of 55 and 75:
- Factors of 55 = 1, 5, 11, 55
- Factors of 75 = 1, 3, 5, 15, 25, 75
Therefore, the GCF of 55 and 75 is 5.
Example 3: The product of two numbers is 4125. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 4125
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 4125/5
Therefore, the LCM is 825.

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FAQs on GCF of 55 and 75

What is the GCF of 55 and 75?

The GCF of 55 and 75 is 5. To calculate the GCF (Greatest Common Factor) of 55 and 75, we need to factor each number (factors of 55 = 1, 5, 11, 55; factors of 75 = 1, 3, 5, 15, 25, 75) and choose the greatest factor that exactly divides both 55 and 75, i.e., 5.

What are the Methods to Find GCF of 55 and 75?

There are three commonly used methods to find the GCF of 55 and 75.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 55 and 75 by Long Division Method?

To find the GCF of 55, 75 using long division method, 75 is divided by 55. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

If the GCF of 75 and 55 is 5, Find its LCM.

GCF(75, 55) × LCM(75, 55) = 75 × 55
Since the GCF of 75 and 55 = 5
⇒ 5 × LCM(75, 55) = 4125
Therefore, LCM = 825
☛ Greatest Common Factor Calculator

How to Find the GCF of 55 and 75 by Prime Factorization?

To find the GCF of 55 and 75, we will find the prime factorization of the given numbers, i.e. 55 = 5 × 11; 75 = 3 × 5 × 5.
⇒ Since 5 is the only common prime factor of 55 and 75. Hence, GCF (55, 75) = 5.
☛ Prime Number

What is the Relation Between LCM and GCF of 55, 75?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 55 and 75, i.e. GCF × LCM = 55 × 75.

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