Highest Common Factor of 423, 709, 584 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 423, 709, 584 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 423, 709, 584 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 423, 709, 584 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 423, 709, 584 is 1.

HCF(423, 709, 584) = 1

HCF of 423, 709, 584 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 423, 709, 584 is 1.

Highest Common Factor of 423,709,584 using Euclid's algorithm

Highest Common Factor of 423,709,584 is 1

Step 1: Since 709 > 423, we apply the division lemma to 709 and 423, to get

709 = 423 x 1 + 286

Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 286 and 423, to get

423 = 286 x 1 + 137

Step 3: We consider the new divisor 286 and the new remainder 137, and apply the division lemma to get

286 = 137 x 2 + 12

We consider the new divisor 137 and the new remainder 12,and apply the division lemma to get

137 = 12 x 11 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 423 and 709 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(137,12) = HCF(286,137) = HCF(423,286) = HCF(709,423) .

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

Step 1: Since 584 > 1, we apply the division lemma to 584 and 1, to get

584 = 1 x 584 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 584 is 1

Notice that 1 = HCF(584,1) .

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Frequently Asked Questions on HCF of 423, 709, 584 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 423, 709, 584?

Answer: HCF of 423, 709, 584 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 423, 709, 584 using Euclid's Algorithm?

Answer: For arbitrary numbers 423, 709, 584 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.