Question

explain Euclid division lemma with examples

Answer 1

EUCLIDS DIVISION LEMMA a=bq+r
where a is dividend
b is. divisor
q is quotient
r is remainder
it is same as
dividend=divisor×quotient +remainder
consider an example where we need to divide 6 with 2
6=2*3+0
hope it helps. ........

Answer 2

According to Euclid’s Division Lemma if we have two positive integers a and b, then there exists unique integers qand r which satisfies the condition a = bq + r where 0 ≤ r ≤ b.
For example:-
FIND HCF OF 12576 and 4052
Step 1 : Since 12576 > 4052, we apply the division lemma to 12576 and 4052, to get
12576 = 4052 × 3 + 420
Step 2 : Since the remainder 420 ≠ 0, we apply the division lemma to 4052 and 420, to get
4052 = 420 × 9 + 272
Step 3 : We consider the new divisor 420 and the new remainder 272, and apply the division lemma to get
420 = 272 × 1 + 148
We consider the new divisor 272 and the new remainder 148, and apply the division lemma to get
272 = 148 × 1 + 124
We consider the new divisor 148 and the new remainder 124, and apply the division lemma to get
148 = 124 × 1 + 24
We consider the new divisor 124 and the new remainder 24, and apply the division lemma to get
124 = 24 × 5 + 4
We consider the new divisor 24 and the new remainder 4, and apply the division lemma to get
24 = 4 × 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 12576 and 4052 is 4.