Question

Define Euclid Devision Lemma. Using this find the HCF of 6 and 8​

Answer 1

Step-by-step explanation:

Correct option is

A

5

According to Euclid’s Division Lemma if we have two positive integers a and b, then there exists unique integers q and r which satisfies the condition a=bq+r where 0≤r≤b.

HCF is the largest number which exactly divides two or more positive integers. By Euclid's division lemma, we mean that on dividing both the integers a and b the remainder is zero.

The given integers are a=65 and b=495.

Clearly 495>65.

So, we will apply Euclid’s division lemma to 65 and 495, we get,

495=(65×7)+40

Since the remainder 40



=0. So we again apply the division lemma to the divisor 65 and remainder 40. We get,

65=(40×1)+25

Again the remainder 25



=0, so applying the division lemma to the new divisor 40 and remainder 25. We get,

40=(25×1)+15

Now, again the remainder 15



=0, so applying the division lemma to the new divisor 25 and remainder 15. We get,

25=(15×1)+10

Again the remainder 10



=0, so applying the division lemma to the new divisor 15 and remainder 10. We get,

15=(10×1)+5

Again the remainder 5



=0, so applying the division lemma to the new divisor 10 and remainder 5. We get,

10=(5×1)+0

Finally we get the remainder 0 and the divisor is 5.

Hence, the HCF of 65 and 495 is 5.

Answer 2

Step-by-step explanation:

6)8(1

6

____

2)6(3

6

___

xx

H.C.F=2 Answer

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