Real Numbers – Notes

Real Numbers- Euclid’s Division Lemma

 Euclid’s division lemma states that for any two positive integers ‘a’ and ‘b’ we can find two whole numbers ‘q’ and ‘r’ such that: a= bq + r, where 0< r < b.

Euclid’s division lemma can be used to find the highest common factor of any two positive integers.

Euclid’s division lemma can be used to show common properties of numbers.

Real Numbers- Fundamental Theorem of Arithmetic

 Fundamental Theorem of Arithmetic states that every composite number can be expressed or factorised as a product of prime numbers and this factorisation is unique except in the order of the prime factors.

HCF of two numbers = The products of Terms containing smallest powers of common Prime Factors of the two numbers.