GCF of 2 and 15
GCF of 2 and 15 is the largest possible number that divides 2 and 15 exactly without any remainder. The factors of 2 and 15 are 1, 2 and 1, 3, 5, 15 respectively. There are 3 commonly used methods to find the GCF of 2 and 15 - Euclidean algorithm, prime factorization, and long division.
1. | GCF of 2 and 15 |
2. | List of Methods |
3. | Solved Examples |
4. | FAQs |
What is GCF of 2 and 15?
Answer: GCF of 2 and 15 is 1.
Explanation:
The GCF of two non-zero integers, x(2) and y(15), is the greatest positive integer m(1) that divides both x(2) and y(15) without any remainder.
Methods to Find GCF of 2 and 15
The methods to find the GCF of 2 and 15 are explained below.
- Listing Common Factors
- Using Euclid's Algorithm
- Long Division Method
GCF of 2 and 15 by Listing Common Factors
- Factors of 2: 1, 2
- Factors of 15: 1, 3, 5, 15
Since, 1 is the only common factor between 2 and 15. The Greatest Common Factor of 2 and 15 is 1.
GCF of 2 and 15 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 = 15 and Y = 2
- GCF(15, 2) = GCF(2, 15 mod 2) = GCF(2, 1)
- GCF(2, 1) = GCF(1, 2 mod 1) = GCF(1, 0)
- GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 2 and 15 is 1.
GCF of 2 and 15 by Long Division
GCF of 2 and 15 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 15 (larger number) by 2 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (2) by the remainder (1).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 2 and 15.
☛ Also Check:
- GCF of 12 and 18 = 6
- GCF of 54 and 90 = 18
- GCF of 49 and 98 = 49
- GCF of 28 and 32 = 4
- GCF of 30 and 54 = 6
- GCF of 14 and 49 = 7
- GCF of 15 and 20 = 5
GCF of 2 and 15 Examples
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Example 1: Find the GCF of 2 and 15, if their LCM is 30.
Solution:
∵ LCM × GCF = 2 × 15
⇒ GCF(2, 15) = (2 × 15)/30 = 1
Therefore, the greatest common factor of 2 and 15 is 1. -
Example 2: Find the greatest number that divides 2 and 15 exactly.
Solution:
The greatest number that divides 2 and 15 exactly is their greatest common factor, i.e. GCF of 2 and 15.
⇒ Factors of 2 and 15:- Factors of 2 = 1, 2
- Factors of 15 = 1, 3, 5, 15
Therefore, the GCF of 2 and 15 is 1.
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Example 3: For two numbers, GCF = 1 and LCM = 30. If one number is 15, find the other number.
Solution:
Given: GCF (z, 15) = 1 and LCM (z, 15) = 30
∵ GCF × LCM = 15 × (z)
⇒ z = (GCF × LCM)/15
⇒ z = (1 × 30)/15
⇒ z = 2
Therefore, the other number is 2.
FAQs on GCF of 2 and 15
What is the GCF of 2 and 15?
The GCF of 2 and 15 is 1. To calculate the GCF of 2 and 15, we need to factor each number (factors of 2 = 1, 2; factors of 15 = 1, 3, 5, 15) and choose the greatest factor that exactly divides both 2 and 15, i.e., 1.
If the GCF of 15 and 2 is 1, Find its LCM.
GCF(15, 2) × LCM(15, 2) = 15 × 2
Since the GCF of 15 and 2 = 1
⇒ 1 × LCM(15, 2) = 30
Therefore, LCM = 30
☛ GCF Calculator
How to Find the GCF of 2 and 15 by Long Division Method?
To find the GCF of 2, 15 using long division method, 15 is divided by 2. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 2 and 15?
There are three commonly used methods to find the GCF of 2 and 15.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
What is the Relation Between LCM and GCF of 2, 15?
The following equation can be used to express the relation between Least Common Multiple and GCF of 2 and 15, i.e. GCF × LCM = 2 × 15.
How to Find the GCF of 2 and 15 by Prime Factorization?
To find the GCF of 2 and 15, we will find the prime factorization of the given numbers, i.e. 2 = 2; 15 = 3 × 5.
⇒ There is no common prime factor for 2 and 15. Hence, GCF (2, 15) = 1.
☛ What are Prime Numbers?
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