Highest Common Factor of 505, 829 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 505, 829 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 505, 829 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 505, 829 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 505, 829 is 1.

HCF(505, 829) = 1

HCF of 505, 829 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 505, 829 is 1.

Highest Common Factor of 505,829 using Euclid's algorithm

Highest Common Factor of 505,829 is 1

Step 1: Since 829 > 505, we apply the division lemma to 829 and 505, to get

829 = 505 x 1 + 324

Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 324 and 505, to get

505 = 324 x 1 + 181

Step 3: We consider the new divisor 324 and the new remainder 181, and apply the division lemma to get

324 = 181 x 1 + 143

We consider the new divisor 181 and the new remainder 143,and apply the division lemma to get

181 = 143 x 1 + 38

We consider the new divisor 143 and the new remainder 38,and apply the division lemma to get

143 = 38 x 3 + 29

We consider the new divisor 38 and the new remainder 29,and apply the division lemma to get

38 = 29 x 1 + 9

We consider the new divisor 29 and the new remainder 9,and apply the division lemma to get

29 = 9 x 3 + 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 505 and 829 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(29,9) = HCF(38,29) = HCF(143,38) = HCF(181,143) = HCF(324,181) = HCF(505,324) = HCF(829,505) .

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Frequently Asked Questions on HCF of 505, 829 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 505, 829?

Answer: HCF of 505, 829 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 505, 829 using Euclid's Algorithm?

Answer: For arbitrary numbers 505, 829 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.