Highest Common Factor of 3968, 7862, 30229 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 3968, 7862, 30229 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3968, 7862, 30229 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 3968, 7862, 30229 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 3968, 7862, 30229 is 1.

HCF(3968, 7862, 30229) = 1

HCF of 3968, 7862, 30229 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 3968, 7862, 30229 is 1.

Highest Common Factor of 3968,7862,30229 using Euclid's algorithm

Highest Common Factor of 3968,7862,30229 is 1

Step 1: Since 7862 > 3968, we apply the division lemma to 7862 and 3968, to get

7862 = 3968 x 1 + 3894

Step 2: Since the reminder 3968 ≠ 0, we apply division lemma to 3894 and 3968, to get

3968 = 3894 x 1 + 74

Step 3: We consider the new divisor 3894 and the new remainder 74, and apply the division lemma to get

3894 = 74 x 52 + 46

We consider the new divisor 74 and the new remainder 46,and apply the division lemma to get

74 = 46 x 1 + 28

We consider the new divisor 46 and the new remainder 28,and apply the division lemma to get

46 = 28 x 1 + 18

We consider the new divisor 28 and the new remainder 18,and apply the division lemma to get

28 = 18 x 1 + 10

We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get

18 = 10 x 1 + 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 3968 and 7862 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(46,28) = HCF(74,46) = HCF(3894,74) = HCF(3968,3894) = HCF(7862,3968) .

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

Step 1: Since 30229 > 2, we apply the division lemma to 30229 and 2, to get

30229 = 2 x 15114 + 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 30229 is 1

Notice that 1 = HCF(2,1) = HCF(30229,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 3968, 7862, 30229 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 3968, 7862, 30229?

Answer: HCF of 3968, 7862, 30229 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3968, 7862, 30229 using Euclid's Algorithm?

Answer: For arbitrary numbers 3968, 7862, 30229 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.