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 nonzero 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

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.

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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