Highest Common Factor of 534, 814, 35 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 534, 814, 35 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 534, 814, 35 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 534, 814, 35 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 534, 814, 35 is 1.

HCF(534, 814, 35) = 1

HCF of 534, 814, 35 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 534, 814, 35 is 1.

Highest Common Factor of 534,814,35 using Euclid's algorithm

Highest Common Factor of 534,814,35 is 1

Step 1: Since 814 > 534, we apply the division lemma to 814 and 534, to get

814 = 534 x 1 + 280

Step 2: Since the reminder 534 ≠ 0, we apply division lemma to 280 and 534, to get

534 = 280 x 1 + 254

Step 3: We consider the new divisor 280 and the new remainder 254, and apply the division lemma to get

280 = 254 x 1 + 26

We consider the new divisor 254 and the new remainder 26,and apply the division lemma to get

254 = 26 x 9 + 20

We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get

26 = 20 x 1 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 534 and 814 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(254,26) = HCF(280,254) = HCF(534,280) = HCF(814,534) .

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

Step 1: Since 35 > 2, we apply the division lemma to 35 and 2, to get

35 = 2 x 17 + 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 35 is 1

Notice that 1 = HCF(2,1) = HCF(35,2) .

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Frequently Asked Questions on HCF of 534, 814, 35 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 534, 814, 35?

Answer: HCF of 534, 814, 35 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 534, 814, 35 using Euclid's Algorithm?

Answer: For arbitrary numbers 534, 814, 35 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.