Highest Common Factor of 829, 977, 204 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 829, 977, 204 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 829, 977, 204 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 829, 977, 204 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 829, 977, 204 is 1.

HCF(829, 977, 204) = 1

HCF of 829, 977, 204 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 829, 977, 204 is 1.

Highest Common Factor of 829,977,204 using Euclid's algorithm

Highest Common Factor of 829,977,204 is 1

Step 1: Since 977 > 829, we apply the division lemma to 977 and 829, to get

977 = 829 x 1 + 148

Step 2: Since the reminder 829 ≠ 0, we apply division lemma to 148 and 829, to get

829 = 148 x 5 + 89

Step 3: We consider the new divisor 148 and the new remainder 89, and apply the division lemma to get

148 = 89 x 1 + 59

We consider the new divisor 89 and the new remainder 59,and apply the division lemma to get

89 = 59 x 1 + 30

We consider the new divisor 59 and the new remainder 30,and apply the division lemma to get

59 = 30 x 1 + 29

We consider the new divisor 30 and the new remainder 29,and apply the division lemma to get

30 = 29 x 1 + 1

We consider the new divisor 29 and the new remainder 1,and apply the division lemma to get

29 = 1 x 29 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 829 and 977 is 1

Notice that 1 = HCF(29,1) = HCF(30,29) = HCF(59,30) = HCF(89,59) = HCF(148,89) = HCF(829,148) = HCF(977,829) .

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

Step 1: Since 204 > 1, we apply the division lemma to 204 and 1, to get

204 = 1 x 204 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 204 is 1

Notice that 1 = HCF(204,1) .

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Frequently Asked Questions on HCF of 829, 977, 204 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 829, 977, 204?

Answer: HCF of 829, 977, 204 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 829, 977, 204 using Euclid's Algorithm?

Answer: For arbitrary numbers 829, 977, 204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.