Highest Common Factor of 930, 204, 409 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 930, 204, 409 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 930, 204, 409 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 930, 204, 409 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 930, 204, 409 is 1.

HCF(930, 204, 409) = 1

HCF of 930, 204, 409 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 930, 204, 409 is 1.

Highest Common Factor of 930,204,409 using Euclid's algorithm

Highest Common Factor of 930,204,409 is 1

Step 1: Since 930 > 204, we apply the division lemma to 930 and 204, to get

930 = 204 x 4 + 114

Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 114 and 204, to get

204 = 114 x 1 + 90

Step 3: We consider the new divisor 114 and the new remainder 90, and apply the division lemma to get

114 = 90 x 1 + 24

We consider the new divisor 90 and the new remainder 24,and apply the division lemma to get

90 = 24 x 3 + 18

We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get

24 = 18 x 1 + 6

We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get

18 = 6 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 930 and 204 is 6

Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(90,24) = HCF(114,90) = HCF(204,114) = HCF(930,204) .

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

Step 1: Since 409 > 6, we apply the division lemma to 409 and 6, to get

409 = 6 x 68 + 1

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, 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 6 and 409 is 1

Notice that 1 = HCF(6,1) = HCF(409,6) .

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Frequently Asked Questions on HCF of 930, 204, 409 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 930, 204, 409?

Answer: HCF of 930, 204, 409 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 930, 204, 409 using Euclid's Algorithm?

Answer: For arbitrary numbers 930, 204, 409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.