In the realm of mathematics, the concept of the highest common factor (HCF) plays a crucial role in simplifying fractions and solving algebraic equations. If you're looking to master this fundamental operation, our comprehensive guide will empower you with the knowledge and techniques you need.
The HCF of two numbers is the largest positive integer that divides both numbers without leaving a remainder. To determine the HCF of 777 and 1147, we can employ various methods, including the Euclidean algorithm and prime factorization.
Number 1 | Number 2 | HCF |
---|---|---|
777 | 1147 | 3 |
Prime Factorization of 777:
Prime Factor | Power |
---|---|
3 | 1 |
7 | 1 |
37 | 1 |
Prime Factorization of 1147:
Prime Factor | Power |
---|---|
3 | 1 |
11 | 1 |
103 | 1 |
Step 1: Identify the Common Prime Factors
Examine the prime factorizations of 777 and 1147 and identify the common prime factor: 3.
Step 2: Calculate the HCF
Multiply the common prime factor by its lowest power, which is 1 in this case, to obtain the HCF of 777 and 1147: 3.
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