Question

The statement ${\rm{dividend = divisor}} \times {\rm{quotient + remainder}}$is called
a) Euclid’s multiplication lemma
b) Euclid’s addition lemma
c) Euclid’s subtraction lemma
d) Euclid’s division lemma

Answer 1

Hint: The formula for euclid’s division lemma is that dividend is equal to sum of product of divisor and quotient and remainder. In mathematics, the Euclid’s subtraction lemma does not exist.

Complete step-by-step solution
There is only one algorithm in mathematics which is division lemma.
Lemma means the statement is proved and the used statement is used for proving other results.
Euclid is the person who found the division lemma. He is a very famous mathematician.
Euclid’s division lemma states that, if we take any two positive integers “$a$” and “$b$”, then there will exist two unique integers “$q$” and “$r$” such that all the two equation which satisfies the condition $a = bq + r$ where, $0 \le r \le b$, $a = {\rm{dividend}}$, $q = {\rm{quotient}}$, $b = {\rm{dividend}}$ and $r = {\rm{remainder}}$.
The euclid’s multiplication lemma does not exist in mathematics.There is no euclid’s addition lemma in mathematics.
The euclid’s subtraction lemma does not exist in mathematics.
Euclid had found only a division algorithm.
The Euclid division algorithm is used to find the highest common factor (HCF) for two positive integers $a$and $b$.

The correct option is (d) which is Euclid’s division algorithm.

Note: In such types of problem, the Euclid division algorithm is used to find the highest common factor$\left( {{\rm{HCF}}} \right)$ for any number in simple and quick way. For computer languages we can use Euclid lemma.