Highest Common Factor of 589, 970, 210 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 589, 970, 210 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 589, 970, 210 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 589, 970, 210 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 589, 970, 210 is 1.

HCF(589, 970, 210) = 1

HCF of 589, 970, 210 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 589, 970, 210 is 1.

Highest Common Factor of 589,970,210 using Euclid's algorithm

Highest Common Factor of 589,970,210 is 1

Step 1: Since 970 > 589, we apply the division lemma to 970 and 589, to get

970 = 589 x 1 + 381

Step 2: Since the reminder 589 ≠ 0, we apply division lemma to 381 and 589, to get

589 = 381 x 1 + 208

Step 3: We consider the new divisor 381 and the new remainder 208, and apply the division lemma to get

381 = 208 x 1 + 173

We consider the new divisor 208 and the new remainder 173,and apply the division lemma to get

208 = 173 x 1 + 35

We consider the new divisor 173 and the new remainder 35,and apply the division lemma to get

173 = 35 x 4 + 33

We consider the new divisor 35 and the new remainder 33,and apply the division lemma to get

35 = 33 x 1 + 2

We consider the new divisor 33 and the new remainder 2,and apply the division lemma to get

33 = 2 x 16 + 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 589 and 970 is 1

Notice that 1 = HCF(2,1) = HCF(33,2) = HCF(35,33) = HCF(173,35) = HCF(208,173) = HCF(381,208) = HCF(589,381) = HCF(970,589) .

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

Step 1: Since 210 > 1, we apply the division lemma to 210 and 1, to get

210 = 1 x 210 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 210 is 1

Notice that 1 = HCF(210,1) .

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Frequently Asked Questions on HCF of 589, 970, 210 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 589, 970, 210?

Answer: HCF of 589, 970, 210 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 589, 970, 210 using Euclid's Algorithm?

Answer: For arbitrary numbers 589, 970, 210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.