Answer
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Hint: In this question use the basic definition of Euclid’s division lemma and apply it for a special condition that is when the unique integer to be found and which satisfies the division lemma is taken as zero.
Complete step-by-step answer:
According to Euclid’s division lemma,
For each pair of positive integers a and b, we can find unique integers p and q satisfying the relation
$a = bp + q$, where $0 \leqslant q \leqslant b$
So if q = 0 then p is the H.C.F of a and b.
The basis of the Euclidean division algorithm is Euclid’s division lemma.
To calculate the highest common factor (H.C.F) of two positive integers a and b we use Euclid’s division algorithm.
H.C.F is the largest number which exactly divides two or more positive integers.
By exactly we mean that on dividing both the integers a and b the remainder is zero.
So this is the required answer.
Hence option (A) is correct.
Note: In questions there may be a term called Euclid’s division algorithm, we must not confuse between Euclid’s division lemma and Euclid’s division algorithm as both are different. Lemma is a proven statement which is used for providing another statement whereas algorithm is a series of well-defined steps which gives a procedure of solution.
Complete step-by-step answer:
According to Euclid’s division lemma,
For each pair of positive integers a and b, we can find unique integers p and q satisfying the relation
$a = bp + q$, where $0 \leqslant q \leqslant b$
So if q = 0 then p is the H.C.F of a and b.
The basis of the Euclidean division algorithm is Euclid’s division lemma.
To calculate the highest common factor (H.C.F) of two positive integers a and b we use Euclid’s division algorithm.
H.C.F is the largest number which exactly divides two or more positive integers.
By exactly we mean that on dividing both the integers a and b the remainder is zero.
So this is the required answer.
Hence option (A) is correct.
Note: In questions there may be a term called Euclid’s division algorithm, we must not confuse between Euclid’s division lemma and Euclid’s division algorithm as both are different. Lemma is a proven statement which is used for providing another statement whereas algorithm is a series of well-defined steps which gives a procedure of solution.
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