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GCF of 10 and 55

GCF of 10 and 55 is the largest possible number that divides 10 and 55 exactly without any remainder. The factors of 10 and 55 are 1, 2, 5, 10 and 1, 5, 11, 55 respectively. There are 3 commonly used methods to find the GCF of 10 and 55 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 10 and 55
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 55?

Answer: GCF of 10 and 55 is 5.

Explanation:

The GCF of two non-zero integers, x(10) and y(55), is the greatest positive integer m(5) that divides both x(10) and y(55) without any remainder.

Methods to Find GCF of 10 and 55

The methods to find the GCF of 10 and 55 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 10 and 55 by Long Division

GCF of 10 and 55 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 55 (larger number) by 10 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (10) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 10 and 55.

GCF of 10 and 55 by Prime Factorization

Prime factorization of 10 and 55 is (2 × 5) and (5 × 11) respectively. As visible, 10 and 55 have only one common prime factor i.e. 5. Hence, the GCF of 10 and 55 is 5.

GCF of 10 and 55 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 = 55 and Y = 10

GCF(55, 10) = GCF(10, 55 mod 10) = GCF(10, 5)
GCF(10, 5) = GCF(5, 10 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 10 and 55 is 5.

☛ Also Check:

GCF of 10 and 55 Examples

Example 1: The product of two numbers is 550. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 550
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 550/5
Therefore, the LCM is 110.
Example 2: Find the GCF of 10 and 55, if their LCM is 110.

Solution:

∵ LCM × GCF = 10 × 55
⇒ GCF(10, 55) = (10 × 55)/110 = 5
Therefore, the greatest common factor of 10 and 55 is 5.
Example 3: Find the greatest number that divides 10 and 55 exactly.

Solution:

The greatest number that divides 10 and 55 exactly is their greatest common factor, i.e. GCF of 10 and 55.
⇒ Factors of 10 and 55:
- Factors of 10 = 1, 2, 5, 10
- Factors of 55 = 1, 5, 11, 55
Therefore, the GCF of 10 and 55 is 5.

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FAQs on GCF of 10 and 55

What is the GCF of 10 and 55?

The GCF of 10 and 55 is 5. To calculate the GCF (Greatest Common Factor) of 10 and 55, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 55 = 1, 5, 11, 55) and choose the greatest factor that exactly divides both 10 and 55, i.e., 5.

What is the Relation Between LCM and GCF of 10, 55?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 10 and 55, i.e. GCF × LCM = 10 × 55.

How to Find the GCF of 10 and 55 by Prime Factorization?

To find the GCF of 10 and 55, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 55 = 5 × 11.
⇒ Since 5 is the only common prime factor of 10 and 55. Hence, GCF (10, 55) = 5.
☛ What is a Prime Number?

What are the Methods to Find GCF of 10 and 55?

There are three commonly used methods to find the GCF of 10 and 55.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 10 and 55 by Long Division Method?

To find the GCF of 10, 55 using long division method, 55 is divided by 10. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

If the GCF of 55 and 10 is 5, Find its LCM.

GCF(55, 10) × LCM(55, 10) = 55 × 10
Since the GCF of 55 and 10 = 5
⇒ 5 × LCM(55, 10) = 550
Therefore, LCM = 110
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