Highest Common Factor of 5782, 7942, 16383 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 5782, 7942, 16383 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5782, 7942, 16383 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 5782, 7942, 16383 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 5782, 7942, 16383 is 1.

HCF(5782, 7942, 16383) = 1

HCF of 5782, 7942, 16383 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 5782, 7942, 16383 is 1.

Highest Common Factor of 5782,7942,16383 using Euclid's algorithm

Highest Common Factor of 5782,7942,16383 is 1

Step 1: Since 7942 > 5782, we apply the division lemma to 7942 and 5782, to get

7942 = 5782 x 1 + 2160

Step 2: Since the reminder 5782 ≠ 0, we apply division lemma to 2160 and 5782, to get

5782 = 2160 x 2 + 1462

Step 3: We consider the new divisor 2160 and the new remainder 1462, and apply the division lemma to get

2160 = 1462 x 1 + 698

We consider the new divisor 1462 and the new remainder 698,and apply the division lemma to get

1462 = 698 x 2 + 66

We consider the new divisor 698 and the new remainder 66,and apply the division lemma to get

698 = 66 x 10 + 38

We consider the new divisor 66 and the new remainder 38,and apply the division lemma to get

66 = 38 x 1 + 28

We consider the new divisor 38 and the new remainder 28,and apply the division lemma to get

38 = 28 x 1 + 10

We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get

28 = 10 x 2 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5782 and 7942 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(38,28) = HCF(66,38) = HCF(698,66) = HCF(1462,698) = HCF(2160,1462) = HCF(5782,2160) = HCF(7942,5782) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 16383 > 2, we apply the division lemma to 16383 and 2, to get

16383 = 2 x 8191 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 16383 is 1

Notice that 1 = HCF(2,1) = HCF(16383,2) .

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Frequently Asked Questions on HCF of 5782, 7942, 16383 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 5782, 7942, 16383?

Answer: HCF of 5782, 7942, 16383 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5782, 7942, 16383 using Euclid's Algorithm?

Answer: For arbitrary numbers 5782, 7942, 16383 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.