HCF of 6 and 7

HCF of 6 and 7 is the largest possible number that divides 6 and 7 exactly without any remainder. The factors of 6 and 7 are 1, 2, 3, 6 and 1, 7 respectively. There are 3 commonly used methods to find the HCF of 6 and 7 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 6 and 7
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 6 and 7?

Answer: HCF of 6 and 7 is 1.

Explanation:

The HCF of two non-zero integers, x(6) and y(7), is the highest positive integer m(1) that divides both x(6) and y(7) without any remainder.

Methods to Find HCF of 6 and 7

The methods to find the HCF of 6 and 7 are explained below.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

HCF of 6 and 7 by Listing Common Factors

Factors of 6: 1, 2, 3, 6
Factors of 7: 1, 7

Since, 1 is the only common factor between 6 and 7. The highest common factor of 6 and 7 is 1.

HCF of 6 and 7 by Long Division

HCF of 6 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 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 6 and 7.

HCF of 6 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 = 6

HCF(7, 6) = HCF(6, 7 mod 6) = HCF(6, 1)
HCF(6, 1) = HCF(1, 6 mod 1) = HCF(1, 0)
HCF(1, 0) = 1 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 6 and 7 is 1.

☛ Also Check:

HCF of 6 and 7 Examples

Example 1: Find the HCF of 6 and 7, if their LCM is 42.

Solution:

∵ LCM × HCF = 6 × 7
⇒ HCF(6, 7) = (6 × 7)/42 = 1
Therefore, the highest common factor of 6 and 7 is 1.
Example 2: The product of two numbers is 42. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 42
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 42/1
Therefore, the LCM is 42.
Example 3: For two numbers, HCF = 1 and LCM = 42. If one number is 6, find the other number.

Solution:

Given: HCF (z, 6) = 1 and LCM (z, 6) = 42
∵ HCF × LCM = 6 × (z)
⇒ z = (HCF × LCM)/6
⇒ z = (1 × 42)/6
⇒ z = 7
Therefore, the other number is 7.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on HCF of 6 and 7

What is the HCF of 6 and 7?

The HCF of 6 and 7 is 1. To calculate the Highest common factor of 6 and 7, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 7 = 1, 7) and choose the highest factor that exactly divides both 6 and 7, i.e., 1.

What is the Relation Between LCM and HCF of 6, 7?

The following equation can be used to express the relation between Least Common Multiple and HCF of 6 and 7, i.e. HCF × LCM = 6 × 7.

How to Find the HCF of 6 and 7 by Prime Factorization?

To find the HCF of 6 and 7, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 7 = 7.
⇒ There is no common prime factor for 6 and 7. Hence, HCF (6, 7) = 1.
☛ What are Prime Numbers?

How to Find the HCF of 6 and 7 by Long Division Method?

To find the HCF of 6, 7 using long division method, 7 is divided by 6. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 6 and 7?

There are three commonly used methods to find the HCF of 6 and 7.

By Prime Factorization
By Long Division
By Listing Common Factors

If the HCF of 7 and 6 is 1, Find its LCM.

HCF(7, 6) × LCM(7, 6) = 7 × 6
Since the HCF of 7 and 6 = 1
⇒ 1 × LCM(7, 6) = 42
Therefore, LCM = 42
☛ HCF Calculator

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum