Math Class 10. Rational Numbers. : Math Class 10. Rational Numbers. Gurukul24x7
HCF
Prime factorization.
What is HCF? : What is HCF? HCF is called the Highest Common Factor between two or more numbers. For example 6 and 8 have the highest common factor as 2.
HCF can be used to write a number in terms of a smaller number. For example, 32= 4 x 8+0, although there are numerous ways to write a number but here we are interested in writing a number using HCF.
Why should you learn HCF? : Why should you learn HCF? Heavily used in math based security.
Your computer security is also determined by numbers and HCF plays a vital role.
Video channels, radio channels are also secured using math. There also HCF plays a vital role.(For example cable television).
Used in security systems employed by banks.
Euclid's Algorithm. : Euclid's Algorithm. An algorithm is a step by step procedure to perform a particular task. For example making food involves well defined steps which need to be followed in a predefined order.
Euclid's algorithm is used to find HCF of two positive integers.
Step 1: Divide the bigger number by smaller one. If the remainder is 0 then smaller number is the HCF otherwise move to step 2.
Step 2: If the remainder is 1 then there's no HCF otherwise make the divisor as bigger and remainder as smaller number. Repeat Step 1.
Prime Factorization. : Prime Factorization. Fundamental Theorem of Arithmetic says that any number can be uniquely factorized into prime numbers. Basically it means all numbers are composite numbers(formed by performing arithmetic operations on other numbers). These composite numbers can't be formed by other numbers but only themselves, thus these are called prime numbers i.e. the most fundamental of the numbers which can't be derived.
For example: 12 = 2 x 2 x 3 but 29 = 29 x 1 since 29 is a prime number.
Implications of prime factors. : Implications of prime factors. Prime factors of any number are unique.
Can be used to know the result of division of large numbers. For example 442 is not divisible by 15, we don't need to compute the large numbers to know this fact.
Easier to find HCF and LCM of large numbers. This property is employed heavily in today's security systems.