What is HCF (Highest Common Factor)? Definition, Meaning & Example
The largest number that divides two or more numbers without leaving a remainder.
TL;DR: The largest number that divides two or more numbers without leaving a remainder.
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HCF (Highest Common Factor): The largest number that divides two or more numbers without leaving a remainder.
Explanation
HCF is also called GCD or Greatest Common Divisor. To find HCF, list all factors of each number and identify the largest common factor. For example, factors of 12 are 1, 2, 3, 4, 6, 12 and factors of 18 are 1, 2, 3, 6, 9, 18, so HCF is 6. HCF is useful for simplifying fractions; for example, 12/18 can be reduced to 2/3 by dividing both by their HCF of 6. Finding HCF helps solve real-world problems like dividing items into equal groups. The Euclidean algorithm is an efficient method for finding HCF of large numbers.
Example
The HCF of 24 and 36 is 12 because 12 is the largest number that divides both 24 and 36 evenly.
Frequently Asked Questions
What is the HCF of two prime numbers?
The HCF of two different prime numbers is always 1 because prime numbers only share the factor 1.
How does HCF help with fractions?
HCF helps reduce fractions to simplest form by dividing both numerator and denominator by their HCF.
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