HCF of 3 and 7
HCF of 3 and 7 is the largest possible number that divides 3 and 7 exactly without any remainder. The factors of 3 and 7 are 1, 3 and 1, 7 respectively. There are 3 commonly used methods to find the HCF of 3 and 7  long division, Euclidean algorithm, and prime factorization.
1.  HCF of 3 and 7 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 3 and 7?
Answer: HCF of 3 and 7 is 1.
Explanation:
The HCF of two nonzero integers, x(3) and y(7), is the highest positive integer m(1) that divides both x(3) and y(7) without any remainder.
Methods to Find HCF of 3 and 7
The methods to find the HCF of 3 and 7 are explained below.
 Long Division Method
 Using Euclid's Algorithm
 Prime Factorization Method
HCF of 3 and 7 by Long Division
HCF of 3 and 7 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 7 (larger number) by 3 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (3) by the remainder (1).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the HCF of 3 and 7.
HCF of 3 and 7 by Euclidean Algorithm
As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 7 and Y = 3
 HCF(7, 3) = HCF(3, 7 mod 3) = HCF(3, 1)
 HCF(3, 1) = HCF(1, 3 mod 1) = HCF(1, 0)
 HCF(1, 0) = 1 (∵ HCF(X, 0) = X, where X ≠ 0)
Therefore, the value of HCF of 3 and 7 is 1.
HCF of 3 and 7 by Prime Factorization
Prime factorization of 3 and 7 is (3) and (7) respectively. As visible, there are no common prime factors between 3 and 7, i.e. they are coprime. Hence, the HCF of 3 and 7 will be 1.
☛ Also Check:
 HCF of 36 and 144 = 36
 HCF of 12 and 14 = 2
 HCF of 34 and 102 = 34
 HCF of 81 and 237 = 3
 HCF of 18 and 27 = 9
 HCF of 324 and 144 = 36
 HCF of 8 and 12 = 4
HCF of 3 and 7 Examples

Example 1: Find the highest number that divides 3 and 7 exactly.
Solution:
The highest number that divides 3 and 7 exactly is their highest common factor, i.e. HCF of 3 and 7.
⇒ Factors of 3 and 7: Factors of 3 = 1, 3
 Factors of 7 = 1, 7
Therefore, the HCF of 3 and 7 is 1.

Example 2: For two numbers, HCF = 1 and LCM = 21. If one number is 7, find the other number.
Solution:
Given: HCF (z, 7) = 1 and LCM (z, 7) = 21
∵ HCF × LCM = 7 × (z)
⇒ z = (HCF × LCM)/7
⇒ z = (1 × 21)/7
⇒ z = 3
Therefore, the other number is 3. 
Example 3: The product of two numbers is 21. If their HCF is 1, what is their LCM?
Solution:
Given: HCF = 1 and product of numbers = 21
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 21/1
Therefore, the LCM is 21.
FAQs on HCF of 3 and 7
What is the HCF of 3 and 7?
The HCF of 3 and 7 is 1. To calculate the HCF of 3 and 7, we need to factor each number (factors of 3 = 1, 3; factors of 7 = 1, 7) and choose the highest factor that exactly divides both 3 and 7, i.e., 1.
What is the Relation Between LCM and HCF of 3, 7?
The following equation can be used to express the relation between LCM and HCF of 3 and 7, i.e. HCF × LCM = 3 × 7.
How to Find the HCF of 3 and 7 by Long Division Method?
To find the HCF of 3, 7 using long division method, 7 is divided by 3. The corresponding divisor (1) when remainder equals 0 is taken as HCF.
If the HCF of 7 and 3 is 1, Find its LCM.
HCF(7, 3) × LCM(7, 3) = 7 × 3
Since the HCF of 7 and 3 = 1
⇒ 1 × LCM(7, 3) = 21
Therefore, LCM = 21
☛ Highest Common Factor Calculator
What are the Methods to Find HCF of 3 and 7?
There are three commonly used methods to find the HCF of 3 and 7.
 By Prime Factorization
 By Euclidean Algorithm
 By Long Division
How to Find the HCF of 3 and 7 by Prime Factorization?
To find the HCF of 3 and 7, we will find the prime factorization of the given numbers, i.e. 3 = 3; 7 = 7.
⇒ There is no common prime factor for 3 and 7. Hence, HCF (3, 7) = 1.
☛ What are Prime Numbers?
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