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HCF of 777 and 1147

HCF of 777 and 1147 is the largest possible number that divides 777 and 1147 exactly without any remainder. The factors of 777 and 1147 are 1, 3, 7, 21, 37, 111, 259, 777 and 1, 31, 37, 1147 respectively. There are 3 commonly used methods to find the HCF of 777 and 1147 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 777 and 1147
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 777 and 1147?

Answer: HCF of 777 and 1147 is 37.

Explanation:

The HCF of two non-zero integers, x(777) and y(1147), is the highest positive integer m(37) that divides both x(777) and y(1147) without any remainder.

Methods to Find HCF of 777 and 1147

Let's look at the different methods for finding the HCF of 777 and 1147.

Using Euclid's Algorithm
Prime Factorization Method
Listing Common Factors

HCF of 777 and 1147 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 = 1147 and Y = 777

HCF(1147, 777) = HCF(777, 1147 mod 777) = HCF(777, 370)
HCF(777, 370) = HCF(370, 777 mod 370) = HCF(370, 37)
HCF(370, 37) = HCF(37, 370 mod 37) = HCF(37, 0)
HCF(37, 0) = 37 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 777 and 1147 is 37.

HCF of 777 and 1147 by Prime Factorization

Prime factorization of 777 and 1147 is (3 × 7 × 37) and (31 × 37) respectively. As visible, 777 and 1147 have only one common prime factor i.e. 37. Hence, the HCF of 777 and 1147 is 37.

HCF of 777 and 1147 by Listing Common Factors

Factors of 777: 1, 3, 7, 21, 37, 111, 259, 777
Factors of 1147: 1, 31, 37, 1147

There are 2 common factors of 777 and 1147, that are 1 and 37. Therefore, the highest common factor of 777 and 1147 is 37.

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HCF of 777 and 1147 Examples

Example 1: The product of two numbers is 891219. If their HCF is 37, what is their LCM?

Solution:

Given: HCF = 37 and product of numbers = 891219
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 891219/37
Therefore, the LCM is 24087.
Example 2: For two numbers, HCF = 37 and LCM = 24087. If one number is 777, find the other number.

Solution:

Given: HCF (x, 777) = 37 and LCM (x, 777) = 24087
∵ HCF × LCM = 777 × (x)
⇒ x = (HCF × LCM)/777
⇒ x = (37 × 24087)/777
⇒ x = 1147
Therefore, the other number is 1147.
Example 3: Find the HCF of 777 and 1147, if their LCM is 24087.

Solution:

∵ LCM × HCF = 777 × 1147
⇒ HCF(777, 1147) = (777 × 1147)/24087 = 37
Therefore, the highest common factor of 777 and 1147 is 37.

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FAQs on HCF of 777 and 1147

What is the HCF of 777 and 1147?

The HCF of 777 and 1147 is 37. To calculate the HCF of 777 and 1147, we need to factor each number (factors of 777 = 1, 3, 7, 21, 37, 111, 259, 777; factors of 1147 = 1, 31, 37, 1147) and choose the highest factor that exactly divides both 777 and 1147, i.e., 37.

How to Find the HCF of 777 and 1147 by Prime Factorization?

To find the HCF of 777 and 1147, we will find the prime factorization of the given numbers, i.e. 777 = 3 × 7 × 37; 1147 = 31 × 37.
⇒ Since 37 is the only common prime factor of 777 and 1147. Hence, HCF (777, 1147) = 37.
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What is the Relation Between LCM and HCF of 777, 1147?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 777 and 1147, i.e. HCF × LCM = 777 × 1147.

What are the Methods to Find HCF of 777 and 1147?

There are three commonly used methods to find the HCF of 777 and 1147.

By Prime Factorization
By Listing Common Factors
By Long Division

How to Find the HCF of 777 and 1147 by Long Division Method?

To find the HCF of 777, 1147 using long division method, 1147 is divided by 777. The corresponding divisor (37) when remainder equals 0 is taken as HCF.

If the HCF of 1147 and 777 is 37, Find its LCM.

HCF(1147, 777) × LCM(1147, 777) = 1147 × 777
Since the HCF of 1147 and 777 = 37
⇒ 37 × LCM(1147, 777) = 891219
Therefore, LCM = 24087
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