Highest Common Factor of 423, 680, 588 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, 680, 588 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 423, 680, 588 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, 680, 588 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, 680, 588 is 1.

HCF(423, 680, 588) = 1

HCF of 423, 680, 588 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, 680, 588 is 1.

Highest Common Factor of 423,680,588 using Euclid's algorithm

Highest Common Factor of 423,680,588 is 1

Step 1: Since 680 > 423, we apply the division lemma to 680 and 423, to get

680 = 423 x 1 + 257

Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 257 and 423, to get

423 = 257 x 1 + 166

Step 3: We consider the new divisor 257 and the new remainder 166, and apply the division lemma to get

257 = 166 x 1 + 91

We consider the new divisor 166 and the new remainder 91,and apply the division lemma to get

166 = 91 x 1 + 75

We consider the new divisor 91 and the new remainder 75,and apply the division lemma to get

91 = 75 x 1 + 16

We consider the new divisor 75 and the new remainder 16,and apply the division lemma to get

75 = 16 x 4 + 11

We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 423 and 680 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(75,16) = HCF(91,75) = HCF(166,91) = HCF(257,166) = HCF(423,257) = HCF(680,423) .

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

Step 1: Since 588 > 1, we apply the division lemma to 588 and 1, to get

588 = 1 x 588 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 588 is 1

Notice that 1 = HCF(588,1) .

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Frequently Asked Questions on HCF of 423, 680, 588 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, 680, 588?

Answer: HCF of 423, 680, 588 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 423, 680, 588 using Euclid's Algorithm?

Answer: For arbitrary numbers 423, 680, 588 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.