Highest Common Factor of 471, 702, 854 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 471, 702, 854 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 471, 702, 854 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 471, 702, 854 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 471, 702, 854 is 1.

HCF(471, 702, 854) = 1

HCF of 471, 702, 854 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 471, 702, 854 is 1.

Highest Common Factor of 471,702,854 using Euclid's algorithm

Highest Common Factor of 471,702,854 is 1

Step 1: Since 702 > 471, we apply the division lemma to 702 and 471, to get

702 = 471 x 1 + 231

Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 231 and 471, to get

471 = 231 x 2 + 9

Step 3: We consider the new divisor 231 and the new remainder 9, and apply the division lemma to get

231 = 9 x 25 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 471 and 702 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(231,9) = HCF(471,231) = HCF(702,471) .

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

Step 1: Since 854 > 3, we apply the division lemma to 854 and 3, to get

854 = 3 x 284 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 854 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(854,3) .

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Frequently Asked Questions on HCF of 471, 702, 854 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 471, 702, 854?

Answer: HCF of 471, 702, 854 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 471, 702, 854 using Euclid's Algorithm?

Answer: For arbitrary numbers 471, 702, 854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.