GCF of 7, 15 and 21
GCF of 7, 15 and 21 is the largest possible number that divides 7, 15 and 21 exactly without any remainder. The factors of 7, 15 and 21 are (1, 7), (1, 3, 5, 15) and (1, 3, 7, 21) respectively. There are 3 commonly used methods to find the GCF of 7, 15 and 21  long division, prime factorization, and Euclidean algorithm.
1.  GCF of 7, 15 and 21 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 7, 15 and 21?
Answer: GCF of 7, 15 and 21 is 1.
Explanation:
The GCF of three nonzero integers, x(7), y(15) and z(21), is the greatest positive integer m(1) that divides x(7), y(15) and z(21) without any remainder.
Methods to Find GCF of 7, 15 and 21
Let's look at the different methods for finding the GCF of 7, 15 and 21.
 Prime Factorization Method
 Long Division Method
 Using Euclid's Algorithm
GCF of 7, 15 and 21 by Prime Factorization
Prime factorization of 7, 15 and 21 is (7), (3 × 5) and (3 × 7) respectively. As visible, there are no common prime factors between 7, 15 and 21, i.e. they are coprime. Hence, the GCF of 7, 15 and 21 will be 1.
GCF of 7, 15 and 21 by Long Division
GCF of 7, 15 and 21 can be represented as GCF of (GCF of 7, 15) and 21. GCF(7, 15, 21) can be thus calculated by first finding GCF(7, 15) using long division and thereafter using this result with 21 to perform long division again.
 Step 1: Divide 15 (larger number) by 7 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (7) by the remainder (1). Repeat this process until the remainder = 0.
⇒ GCF(7, 15) = 1.  Step 3: Now to find the GCF of 1 and 21, we will perform a long division on 21 and 1.
 Step 4: For remainder = 0, divisor = 1 ⇒ GCF(1, 21) = 1
Thus, GCF(7, 15, 21) = GCF(GCF(7, 15), 21) = 1.
GCF of 7, 15 and 21 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.
GCF(7, 15, 21) = GCF(GCF(7, 15), 21)
 GCF(15, 7) = GCF(7, 15 mod 7) = GCF(7, 1)
 GCF(7, 1) = GCF(1, 7 mod 1) = GCF(1, 0)
 GCF(1, 0) = 1 (∵ GCF(X, 0) = X, where X ≠ 0)
Steps for GCF(1, 21)
 GCF(21, 1) = GCF(1, 21 mod 1) = GCF(1, 0)
 GCF(1, 0) = 1 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 7, 15 and 21 is 1.
☛ Also Check:
 GCF of 30 and 50 = 10
 GCF of 60 and 84 = 12
 GCF of 56 and 35 = 7
 GCF of 10 and 50 = 10
 GCF of 50 and 72 = 2
 GCF of 8 and 20 = 4
 GCF of 8 and 40 = 8
GCF of 7, 15 and 21 Examples

Example 1: Calculate the GCF of 7, 15, and 21 using LCM of the given numbers.
Solution:
Prime factorization of 7, 15 and 21 is given as,
 7 = 7
 15 = 3 × 5
 21 = 3 × 7
LCM(7, 15) = 105, LCM(15, 21) = 105, LCM(21, 7) = 21, LCM(7, 15, 21) = 105
⇒ GCF(7, 15, 21) = [(7 × 15 × 21) × LCM(7, 15, 21)]/[LCM(7, 15) × LCM (15, 21) × LCM(21, 7)]
⇒ GCF(7, 15, 21) = (2205 × 105)/(105 × 105 × 21)
⇒ GCF(7, 15, 21) = 1.
Therefore, the GCF of 7, 15 and 21 is 1. 
Example 2: Find the greatest number that divides 7, 15, and 21 completely.
Solution:
The greatest number that divides 7, 15, and 21 exactly is their greatest common factor.
 Factors of 7 = 1, 7
 Factors of 15 = 1, 3, 5, 15
 Factors of 21 = 1, 3, 7, 21
The GCF of 7, 15, and 21 is 1.
∴ The greatest number that divides 7, 15, and 21 is 1. 
Example 3: Verify the relation between the LCM and GCF of 7, 15 and 21.
Solution:
The relation between the LCM and GCF of 7, 15 and 21 is given as, GCF(7, 15, 21) = [(7 × 15 × 21) × LCM(7, 15, 21)]/[LCM(7, 15) × LCM (15, 21) × LCM(7, 21)]
⇒ Prime factorization of 7, 15 and 21: 7 = 7
 15 = 3 × 5
 21 = 3 × 7
∴ LCM of (7, 15), (15, 21), (7, 21), and (7, 15, 21) is 105, 105, 21, and 105 respectively.
Now, LHS = GCF(7, 15, 21) = 1.
And, RHS = [(7 × 15 × 21) × LCM(7, 15, 21)]/[LCM(7, 15) × LCM (15, 21) × LCM(7, 21)] = [(2205) × 105]/[105 × 105 × 21]
LHS = RHS = 1.
Hence verified.
FAQs on GCF of 7, 15 and 21
What is the GCF of 7, 15 and 21?
The GCF of 7, 15 and 21 is 1. To calculate the GCF of 7, 15 and 21, we need to factor each number (factors of 7 = 1, 7; factors of 15 = 1, 3, 5, 15; factors of 21 = 1, 3, 7, 21) and choose the greatest factor that exactly divides 7, 15 and 21, i.e., 1.
What is the Relation Between LCM and GCF of 7, 15 and 21?
The following equation can be used to express the relation between Least Common Multiple and GCF of 7, 15 and 21, i.e. GCF(7, 15, 21) = [(7 × 15 × 21) × LCM(7, 15, 21)]/[LCM(7, 15) × LCM (15, 21) × LCM(7, 21)].
☛ GCF Calculator
Which of the following is GCF of 7, 15 and 21? 1, 60, 32, 56, 66, 40, 61
GCF of 7, 15, 21 will be the number that divides 7, 15, and 21 without leaving any remainder. The only number that satisfies the given condition is 1.
How to Find the GCF of 7, 15 and 21 by Prime Factorization?
To find the GCF of 7, 15 and 21, we will find the prime factorization of given numbers, i.e. 7 = 7; 15 = 3 × 5; 21 = 3 × 7.
⇒ There is no common prime factor for 7, 15 and 21. Hence, GCF(7, 15, 21) = 1.
☛ What is a Prime Number?
What are the Methods to Find GCF of 7, 15 and 21?
There are three commonly used methods to find the GCF of 7, 15 and 21.
 By Prime Factorization
 By Listing Common Factors
 By Long Division