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 Euclid’s division lemma can be used to: Check the value of ‘r’. If ‘r’ is equal to zero then ‘b’ is the HCF of the given numbers. If ‘r’ is not equal to zero, apply Euclid’s division lemma to the new divisor ‘b’ and remainder ‘r’. Continue this process till the remainder ‘r’ becomes zero. The value of the divisor ‘b’ in that case is the HCF of the two given numbers. plz thumbs upEuclid's Division Lemma
Find the highest common factor of any two positive integers and to show the common properties of numbers.
Finding H.C.F using Euclid’s division lemma:
Suppose, we have two positive integers ‘a’ and ‘b’ such that ‘a’ is greater than ‘b’. Apply Euclid’s division lemma to the given integers ‘a’ and ‘b’ to find two whole numbers ‘q’ and ‘r’ such that, ‘a’ is equal to ‘b’ multiplied by ‘q’ plus ‘r’.
Euclid’s division algorithm can also be used to find some common properties of numbers.
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Introduction: In mathematics, Euclid's lemma is most important lemma as regards divisibility and prim numbers. In simplest form, lemma states that a prime number that divides a product of two integers have to divide one of the two integers. This key fact requires a amazingly sophisticated proof and is a wanted step in the ordinary proof of the fundamental theorem of arithmetic. Euclid's lemma in plain language says: If a number N is a multiple of a prime number p, and N = a · b, then at least one of a and b must be a multiple of p. Say, N=56 p=7 Then either or Obviously, in this case, 7 divides 14 (x = 2). plz thumbs up Euclid's Division Lemma
Euclid’s Division Lemma
Find maximum regular factor of any two positive integers and to show regular properties of numbers.
Suppose, we hold two positive integers a and b such that a is greater than b. Apply Euclid’s division lemma to specified integers a and b to find two full numbers q and r such that, a is equal to b multiplied by q plus r.
Euclid’s division algorithm can be used to find some regular properties of numbers.Example
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