Highest Common Factor of 864, 805, 106 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 864, 805, 106 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 864, 805, 106 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 864, 805, 106 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 864, 805, 106 is 1.

HCF(864, 805, 106) = 1

HCF of 864, 805, 106 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 864, 805, 106 is 1.

Highest Common Factor of 864,805,106 using Euclid's algorithm

Highest Common Factor of 864,805,106 is 1

Step 1: Since 864 > 805, we apply the division lemma to 864 and 805, to get

864 = 805 x 1 + 59

Step 2: Since the reminder 805 ≠ 0, we apply division lemma to 59 and 805, to get

805 = 59 x 13 + 38

Step 3: We consider the new divisor 59 and the new remainder 38, and apply the division lemma to get

59 = 38 x 1 + 21

We consider the new divisor 38 and the new remainder 21,and apply the division lemma to get

38 = 21 x 1 + 17

We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get

21 = 17 x 1 + 4

We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get

17 = 4 x 4 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 864 and 805 is 1

Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(38,21) = HCF(59,38) = HCF(805,59) = HCF(864,805) .

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

Step 1: Since 106 > 1, we apply the division lemma to 106 and 1, to get

106 = 1 x 106 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 106 is 1

Notice that 1 = HCF(106,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 864, 805, 106 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 864, 805, 106?

Answer: HCF of 864, 805, 106 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 864, 805, 106 using Euclid's Algorithm?

Answer: For arbitrary numbers 864, 805, 106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.