Highest Common Factor of 710, 971, 810 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 710, 971, 810 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 710, 971, 810 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 710, 971, 810 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 710, 971, 810 is 1.

HCF(710, 971, 810) = 1

HCF of 710, 971, 810 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 710, 971, 810 is 1.

Highest Common Factor of 710,971,810 using Euclid's algorithm

Highest Common Factor of 710,971,810 is 1

Step 1: Since 971 > 710, we apply the division lemma to 971 and 710, to get

971 = 710 x 1 + 261

Step 2: Since the reminder 710 ≠ 0, we apply division lemma to 261 and 710, to get

710 = 261 x 2 + 188

Step 3: We consider the new divisor 261 and the new remainder 188, and apply the division lemma to get

261 = 188 x 1 + 73

We consider the new divisor 188 and the new remainder 73,and apply the division lemma to get

188 = 73 x 2 + 42

We consider the new divisor 73 and the new remainder 42,and apply the division lemma to get

73 = 42 x 1 + 31

We consider the new divisor 42 and the new remainder 31,and apply the division lemma to get

42 = 31 x 1 + 11

We consider the new divisor 31 and the new remainder 11,and apply the division lemma to get

31 = 11 x 2 + 9

We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get

11 = 9 x 1 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 1

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 710 and 971 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(31,11) = HCF(42,31) = HCF(73,42) = HCF(188,73) = HCF(261,188) = HCF(710,261) = HCF(971,710) .

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

Step 1: Since 810 > 1, we apply the division lemma to 810 and 1, to get

810 = 1 x 810 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 810 is 1

Notice that 1 = HCF(810,1) .

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Frequently Asked Questions on HCF of 710, 971, 810 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 710, 971, 810?

Answer: HCF of 710, 971, 810 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 710, 971, 810 using Euclid's Algorithm?

Answer: For arbitrary numbers 710, 971, 810 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.