Question

Use Euclid's algorithm to find the HCF of 40520and 12576.​

Answer 1

Answer:

4

Step-by-step explanation:

According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist 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.

Since 12576 > 4052

12576 = (4052 × 3) + 420

420 is a reminder which is not equal to zero (420 ≠ 0).

4052 = (420 × 9) + 272

271 is a reminder which is not equal to zero (272 ≠ 0).

Now consider the new divisor 272 and the new remainder 148.

272 = (148 × 1) + 124

Now consider the new divisor 148 and the new remainder 124.

148 = (124 × 1) + 24

Now consider the new divisor 124 and the new remainder 24.  

124 = (24 × 5) + 4  

Now consider the new divisor 24 and the new remainder 4.  

24 = (4 × 6) + 0  

Reminder = 0  

Divisor = 4  

HCF of 12576 and 4052 = 4.

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Answer 2

Here 40520 is greater than 12576
Now, consider the largest number as 'a' from the given number ie., 40520 and 12576 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b
Step 1: Since 40520 > 12576, we apply the division lemma to 40520 and 12576, to get
40520 = 12576 x 3 + 2792
Step 2: Since the reminder 12576 ≠ 0, we apply division lemma to 2792 and 12576, to get
12576 = 2792 x 4 + 1408
Step 3: We consider the new divisor 2792 and the new remainder 1408, and apply the division lemma to get
2792 = 1408 x 1 + 1384
We consider the new divisor 1408 and the new remainder 1384,and apply the division lemma to get
1408 = 1384 x 1 + 24
We consider the new divisor 1384 and the new remainder 24,and apply the division lemma to get
1384 = 24 x 57 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 40520 and 12576 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(1384,24) = HCF(1408,1384) = HCF(2792,1408) = HCF(12576,2792) = HCF(40520,12576) .
Therefore, HCF of 40520,12576 using Euclid's division lemma is 8.