Highest Common Factor of 589, 378, 159 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, 378, 159 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 589, 378, 159 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, 378, 159 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, 378, 159 is 1.

HCF(589, 378, 159) = 1

HCF of 589, 378, 159 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, 378, 159 is 1.

Highest Common Factor of 589,378,159 using Euclid's algorithm

Highest Common Factor of 589,378,159 is 1

Step 1: Since 589 > 378, we apply the division lemma to 589 and 378, to get

589 = 378 x 1 + 211

Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 211 and 378, to get

378 = 211 x 1 + 167

Step 3: We consider the new divisor 211 and the new remainder 167, and apply the division lemma to get

211 = 167 x 1 + 44

We consider the new divisor 167 and the new remainder 44,and apply the division lemma to get

167 = 44 x 3 + 35

We consider the new divisor 44 and the new remainder 35,and apply the division lemma to get

44 = 35 x 1 + 9

We consider the new divisor 35 and the new remainder 9,and apply the division lemma to get

35 = 9 x 3 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 589 and 378 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(35,9) = HCF(44,35) = HCF(167,44) = HCF(211,167) = HCF(378,211) = HCF(589,378) .

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

Step 1: Since 159 > 1, we apply the division lemma to 159 and 1, to get

159 = 1 x 159 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 159 is 1

Notice that 1 = HCF(159,1) .

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Frequently Asked Questions on HCF of 589, 378, 159 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, 378, 159?

Answer: HCF of 589, 378, 159 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 589, 378, 159 using Euclid's Algorithm?

Answer: For arbitrary numbers 589, 378, 159 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.