Highest Common Factor of 831, 514, 12, 669 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 831, 514, 12, 669 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 831, 514, 12, 669 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 831, 514, 12, 669 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 831, 514, 12, 669 is 1.

HCF(831, 514, 12, 669) = 1

HCF of 831, 514, 12, 669 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 831, 514, 12, 669 is 1.

Highest Common Factor of 831,514,12,669 using Euclid's algorithm

Highest Common Factor of 831,514,12,669 is 1

Step 1: Since 831 > 514, we apply the division lemma to 831 and 514, to get

831 = 514 x 1 + 317

Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 317 and 514, to get

514 = 317 x 1 + 197

Step 3: We consider the new divisor 317 and the new remainder 197, and apply the division lemma to get

317 = 197 x 1 + 120

We consider the new divisor 197 and the new remainder 120,and apply the division lemma to get

197 = 120 x 1 + 77

We consider the new divisor 120 and the new remainder 77,and apply the division lemma to get

120 = 77 x 1 + 43

We consider the new divisor 77 and the new remainder 43,and apply the division lemma to get

77 = 43 x 1 + 34

We consider the new divisor 43 and the new remainder 34,and apply the division lemma to get

43 = 34 x 1 + 9

We consider the new divisor 34 and the new remainder 9,and apply the division lemma to get

34 = 9 x 3 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 831 and 514 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(34,9) = HCF(43,34) = HCF(77,43) = HCF(120,77) = HCF(197,120) = HCF(317,197) = HCF(514,317) = HCF(831,514) .

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

Step 1: Since 12 > 1, we apply the division lemma to 12 and 1, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12 is 1

Notice that 1 = HCF(12,1) .

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

Step 1: Since 669 > 1, we apply the division lemma to 669 and 1, to get

669 = 1 x 669 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 669 is 1

Notice that 1 = HCF(669,1) .

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Frequently Asked Questions on HCF of 831, 514, 12, 669 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 831, 514, 12, 669?

Answer: HCF of 831, 514, 12, 669 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 831, 514, 12, 669 using Euclid's Algorithm?

Answer: For arbitrary numbers 831, 514, 12, 669 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.