GCF of 2 and 10 is the largest possible number that divides 2 and 10 exactly without any remainder. The factors of 2 and 10 are 1, 2 and 1, 2, 5, 10 respectively. There are 3 commonly used methods to find the GCF of 2 and 10 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 2 and 10 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 2 and 10?
Answer: GCF of 2 and 10 is 2.
Explanation:
The GCF of two non-zero integers, x(2) and y(10), is the greatest positive integer m(2) that divides both x(2) and y(10) without any remainder.
Methods to Find GCF of 2 and 10
Let's look at the different methods for finding the GCF of 2 and 10.
- Prime Factorization Method
- Using Euclid's Algorithm
- Listing Common Factors
GCF of 2 and 10 by Prime Factorization
Prime factorization of 2 and 10 is (2) and (2 × 5) respectively. As visible, 2 and 10 have only one common prime factor i.e. 2. Hence, the GCF of 2 and 10 is 2.
GCF of 2 and 10 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 = 10 and Y = 2
- GCF(10, 2) = GCF(2, 10 mod 2) = GCF(2, 0)
- GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 2 and 10 is 2.
GCF of 2 and 10 by Listing Common Factors
- Factors of 2: 1, 2
- Factors of 10: 1, 2, 5, 10
There are 2 common factors of 2 and 10, that are 1 and 2. Therefore, the greatest common factor of 2 and 10 is 2.
☛ Also Check:
- GCF of 28 and 63 = 7
- GCF of 42 and 60 = 6
- GCF of 36 and 96 = 12
- GCF of 45 and 63 = 9
- GCF of 81 and 108 = 27
- GCF of 42 and 70 = 14
- GCF of 27 and 72 = 9
GCF of 2 and 10 Examples
Example 1: Find the greatest number that divides 2 and 10 exactly.
Solution:
The greatest number that divides 2 and 10 exactly is their greatest common factor, i.e. GCF of 2 and 10.
⇒ Factors of 2 and 10:- Factors of 2 = 1, 2
- Factors of 10 = 1, 2, 5, 10
Therefore, the GCF of 2 and 10 is 2.
Example 2: The product of two numbers is 20. If their GCF is 2, what is their LCM?
Solution:
Given: GCF = 2 and product of numbers = 20
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 20/2
Therefore, the LCM is 10.Example 3: For two numbers, GCF = 2 and LCM = 10. If one number is 2, find the other number.
Solution:
Given: GCF (y, 2) = 2 and LCM (y, 2) = 10
∵ GCF × LCM = 2 × (y)
⇒ y = (GCF × LCM)/2
⇒ y = (2 × 10)/2
⇒ y = 10
Therefore, the other number is 10.
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FAQs on GCF of 2 and 10
What is the GCF of 2 and 10?
The GCF of 2 and 10 is 2. To calculate the greatest common factor of 2 and 10, we need to factor each number (factors of 2 = 1, 2; factors of 10 = 1, 2, 5, 10) and choose the greatest factor that exactly divides both 2 and 10, i.e., 2.
How to Find the GCF of 2 and 10 by Long Division Method?
To find the GCF of 2, 10 using long division method, 10 is divided by 2. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
If the GCF of 10 and 2 is 2, Find its LCM.
GCF(10, 2) × LCM(10, 2) = 10 × 2
Since the GCF of 10 and 2 = 2
⇒ 2 × LCM(10, 2) = 20
Therefore, LCM = 10
☛ Greatest Common Factor Calculator
What are the Methods to Find GCF of 2 and 10?
There are three commonly used methods to find the GCF of 2 and 10.
- By Listing Common Factors
- By Long Division
- By Prime Factorization
How to Find the GCF of 2 and 10 by Prime Factorization?
To find the GCF of 2 and 10, we will find the prime factorization of the given numbers, i.e. 2 = 2; 10 = 2 × 5.
⇒ Since 2 is the only common prime factor of 2 and 10. Hence, GCF (2, 10) = 2.
☛ What are Prime Numbers?
What is the Relation Between LCM and GCF of 2, 10?
The following equation can be used to express the relation between Least Common Multiple and GCF of 2 and 10, i.e. GCF × LCM = 2 × 10.
