Highest Common Factor of 509, 838 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 509, 838 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 509, 838 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 509, 838 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 509, 838 is 1.

HCF(509, 838) = 1

HCF of 509, 838 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 509, 838 is 1.

Highest Common Factor of 509,838 using Euclid's algorithm

Highest Common Factor of 509,838 is 1

Step 1: Since 838 > 509, we apply the division lemma to 838 and 509, to get

838 = 509 x 1 + 329

Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 329 and 509, to get

509 = 329 x 1 + 180

Step 3: We consider the new divisor 329 and the new remainder 180, and apply the division lemma to get

329 = 180 x 1 + 149

We consider the new divisor 180 and the new remainder 149,and apply the division lemma to get

180 = 149 x 1 + 31

We consider the new divisor 149 and the new remainder 31,and apply the division lemma to get

149 = 31 x 4 + 25

We consider the new divisor 31 and the new remainder 25,and apply the division lemma to get

31 = 25 x 1 + 6

We consider the new divisor 25 and the new remainder 6,and apply the division lemma to get

25 = 6 x 4 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 509 and 838 is 1

Notice that 1 = HCF(6,1) = HCF(25,6) = HCF(31,25) = HCF(149,31) = HCF(180,149) = HCF(329,180) = HCF(509,329) = HCF(838,509) .

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Frequently Asked Questions on HCF of 509, 838 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 509, 838?

Answer: HCF of 509, 838 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 509, 838 using Euclid's Algorithm?

Answer: For arbitrary numbers 509, 838 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.