Euclid division Lemma
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Step-by-step explanation:
Let a and bany positive integer .there exist unique integer p and q.a=bq+r.
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This is the Euclid's Division Lemma
Let Α and Β be two numbers, where A is greater than B
Q → Quotient
R → Remainder
S → Highest divisor divided by the dividend
A = BQ + R₁ { 0 ≤ R₁ < B }
HCF using Euclid's Division Lemma
STEP 1 → Apply the algorithm A = BQ + R₁ { 0 ≤ R₁ < B }
STEP 2 → If R₁ = 0, then B is the HCF of A and B.
STEP 3 → If R₁ ≠ 0, then apply the algorithm to divisor to B and remainder R₁
→ B = R₁ X S + R₂
STEP 4 → Continue this method until the remainder comes 0 ( zero ). Here the last divisor will be the HCF of A and B
EXAMPLE → Find the HCF of 81 and 675 using the
Euclid's Division Lemma
81 < 675
So, A => 675
B => 81
A = BQ + R₁
675 = 81 X 8 { 648 } + 27
81 = 27 X 3 + 0
HCF of 27
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