# state-euclids-division-lemma-is-euclids-lemma-is-used-for-is-greater-than-b-as-a-bqr-then-which-of-abor-r-is-necessarily-zero

A dividend can be written as, Dividend = Divisor × Quotient + Remainder. This brings to 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 = b × q + r where 0 ≤ r < b. Here, Divisor is represented by b x q.

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