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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 non-zero 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 co-prime. Hence, the HCF of 3 and 7 will be 1.

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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.

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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
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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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