Highest Common Factor of 3822, 6968, 65337 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 3822, 6968, 65337 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3822, 6968, 65337 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 3822, 6968, 65337 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 3822, 6968, 65337 is 1.

HCF(3822, 6968, 65337) = 1

HCF of 3822, 6968, 65337 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 3822, 6968, 65337 is 1.

Highest Common Factor of 3822,6968,65337 using Euclid's algorithm

Highest Common Factor of 3822,6968,65337 is 1

Step 1: Since 6968 > 3822, we apply the division lemma to 6968 and 3822, to get

6968 = 3822 x 1 + 3146

Step 2: Since the reminder 3822 ≠ 0, we apply division lemma to 3146 and 3822, to get

3822 = 3146 x 1 + 676

Step 3: We consider the new divisor 3146 and the new remainder 676, and apply the division lemma to get

3146 = 676 x 4 + 442

We consider the new divisor 676 and the new remainder 442,and apply the division lemma to get

676 = 442 x 1 + 234

We consider the new divisor 442 and the new remainder 234,and apply the division lemma to get

442 = 234 x 1 + 208

We consider the new divisor 234 and the new remainder 208,and apply the division lemma to get

234 = 208 x 1 + 26

We consider the new divisor 208 and the new remainder 26,and apply the division lemma to get

208 = 26 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 3822 and 6968 is 26

Notice that 26 = HCF(208,26) = HCF(234,208) = HCF(442,234) = HCF(676,442) = HCF(3146,676) = HCF(3822,3146) = HCF(6968,3822) .

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

Step 1: Since 65337 > 26, we apply the division lemma to 65337 and 26, to get

65337 = 26 x 2512 + 25

Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 25 and 26, to get

26 = 25 x 1 + 1

Step 3: We consider the new divisor 25 and the new remainder 1, and apply the division lemma to get

25 = 1 x 25 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 26 and 65337 is 1

Notice that 1 = HCF(25,1) = HCF(26,25) = HCF(65337,26) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 3822, 6968, 65337 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 3822, 6968, 65337?

Answer: HCF of 3822, 6968, 65337 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3822, 6968, 65337 using Euclid's Algorithm?

Answer: For arbitrary numbers 3822, 6968, 65337 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.