Highest Common Factor of 430, 8205, 8769 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 430, 8205, 8769 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 430, 8205, 8769 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 430, 8205, 8769 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 430, 8205, 8769 is 1.

HCF(430, 8205, 8769) = 1

HCF of 430, 8205, 8769 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 430, 8205, 8769 is 1.

Highest Common Factor of 430,8205,8769 using Euclid's algorithm

Highest Common Factor of 430,8205,8769 is 1

Step 1: Since 8205 > 430, we apply the division lemma to 8205 and 430, to get

8205 = 430 x 19 + 35

Step 2: Since the reminder 430 ≠ 0, we apply division lemma to 35 and 430, to get

430 = 35 x 12 + 10

Step 3: We consider the new divisor 35 and the new remainder 10, and apply the division lemma to get

35 = 10 x 3 + 5

We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 430 and 8205 is 5

Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(430,35) = HCF(8205,430) .

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

Step 1: Since 8769 > 5, we apply the division lemma to 8769 and 5, to get

8769 = 5 x 1753 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: 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 5 and 8769 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(8769,5) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 430, 8205, 8769 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 430, 8205, 8769?

Answer: HCF of 430, 8205, 8769 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 430, 8205, 8769 using Euclid's Algorithm?

Answer: For arbitrary numbers 430, 8205, 8769 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.