All Formula of real numbers

HCF of two positive integers can be find using the Euclid’s Division Lemma algorithm
We know that for any two integers a. b. we can write following expression

a=bq + r , 0≤r<b
If r=0 .then
HCF( a. b) =b
If r≠0 , then
HCF ( a. b) = HCF ( b.r)
Again expressing the integer b.r in Euclid’s Division Lemma, we get
b=pr + r1
HCF ( b,r)=HCF (r,r1)

Similarly successive Euclid’s division can be written until we get the remainder zero, the divisor at that point is called the HCF of the a and b

• HCF (a,b) =1 –  Then a and b are co primes.

• Product of primes Theorem of Arithmetic – Composite Number = Product of Primes

• HCF and LCM by prime factorization method:
  HCF = Product of the smallest power of each common factor in the numbers
  LCM = Product of the greatest power of each prime factor involved in the number

• Important Formula HCF (a,b) X LCM (a,b) =a X b

• Important concept for rational Number  – Terminating decimal expression can be written in the form p/2ⁿ5^m