Question

FIND HCF OF 217 AND 390 BY USING EDL ​

Answer 1

Answer:

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HCF of 217, 39 using Euclid's algorithm

HCF of 217, 39 by Euclid's Divison lemma method can be determined easily by using our free online HCF using Euclid's Divison Lemma Calculator and get the result in a fraction of seconds ie., 1 the largest factor that exactly divides the numbers with r=0.

Highest common factor (HCF) of 217, 39 is 1.

HCF(217, 39) = 1

Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345

Below detailed show work will make you learn how to find HCF of 217,39 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(217,39).

Here 217 is greater than 39

Now, consider the largest number as 'a' from the given number ie., 217 and 39 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 217 > 39, we apply the division lemma to 217 and 39, to get

217 = 39 x 5 + 22

Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 22 and 39, to get

39 = 22 x 1 + 17

Step 3: We consider the new divisor 22 and the new remainder 17, and apply the division lemma to get

22 = 17 x 1 + 5

We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get

17 = 5 x 3 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 217 and 39 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(39,22) = HCF(217,39) .

Therefore, HCF of 217,39 using Euclid's division lemma is 1.

Answer 2

Answer:

Here 390 is greater than 217

Now, consider the largest number as 'a' from the given number ie., 390 and 217 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 390 > 217, we apply the division lemma to 390 and 217, to get

390 = 217 x 1 + 173

Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 173 and 217, to get

217 = 173 x 1 + 44

Step 3: We consider the new divisor 173 and the new remainder 44, and apply the division lemma to get

173 = 44 x 3 + 41

We consider the new divisor 44 and the new remainder 41,and apply the division lemma to get

44 = 41 x 1 + 3

We consider the new divisor 41 and the new remainder 3,and apply the division lemma to get

41 = 3 x 13 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 217 and 390 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(41,3) = HCF(44,41) = HCF(173,44) = HCF(217,173) = HCF(390,217) .

Therefore, HCF of 217,390 using Euclid's division lemma is 1.

Step-by-step explanation:

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