Highest Common Factor of 714, 843, 851 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 714, 843, 851 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 714, 843, 851 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 714, 843, 851 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 714, 843, 851 is 1.

HCF(714, 843, 851) = 1

HCF of 714, 843, 851 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 714, 843, 851 is 1.

Highest Common Factor of 714,843,851 using Euclid's algorithm

Highest Common Factor of 714,843,851 is 1

Step 1: Since 843 > 714, we apply the division lemma to 843 and 714, to get

843 = 714 x 1 + 129

Step 2: Since the reminder 714 ≠ 0, we apply division lemma to 129 and 714, to get

714 = 129 x 5 + 69

Step 3: We consider the new divisor 129 and the new remainder 69, and apply the division lemma to get

129 = 69 x 1 + 60

We consider the new divisor 69 and the new remainder 60,and apply the division lemma to get

69 = 60 x 1 + 9

We consider the new divisor 60 and the new remainder 9,and apply the division lemma to get

60 = 9 x 6 + 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 714 and 843 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(60,9) = HCF(69,60) = HCF(129,69) = HCF(714,129) = HCF(843,714) .

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

Step 1: Since 851 > 3, we apply the division lemma to 851 and 3, to get

851 = 3 x 283 + 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 851 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(851,3) .

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Frequently Asked Questions on HCF of 714, 843, 851 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 714, 843, 851?

Answer: HCF of 714, 843, 851 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 714, 843, 851 using Euclid's Algorithm?

Answer: For arbitrary numbers 714, 843, 851 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.