Highest Common Factor of 840, 529, 617 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 840, 529, 617 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 840, 529, 617 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 840, 529, 617 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 840, 529, 617 is 1.

HCF(840, 529, 617) = 1

HCF of 840, 529, 617 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 840, 529, 617 is 1.

Highest Common Factor of 840,529,617 using Euclid's algorithm

Highest Common Factor of 840,529,617 is 1

Step 1: Since 840 > 529, we apply the division lemma to 840 and 529, to get

840 = 529 x 1 + 311

Step 2: Since the reminder 529 ≠ 0, we apply division lemma to 311 and 529, to get

529 = 311 x 1 + 218

Step 3: We consider the new divisor 311 and the new remainder 218, and apply the division lemma to get

311 = 218 x 1 + 93

We consider the new divisor 218 and the new remainder 93,and apply the division lemma to get

218 = 93 x 2 + 32

We consider the new divisor 93 and the new remainder 32,and apply the division lemma to get

93 = 32 x 2 + 29

We consider the new divisor 32 and the new remainder 29,and apply the division lemma to get

32 = 29 x 1 + 3

We consider the new divisor 29 and the new remainder 3,and apply the division lemma to get

29 = 3 x 9 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 840 and 529 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(29,3) = HCF(32,29) = HCF(93,32) = HCF(218,93) = HCF(311,218) = HCF(529,311) = HCF(840,529) .

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

Step 1: Since 617 > 1, we apply the division lemma to 617 and 1, to get

617 = 1 x 617 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 617 is 1

Notice that 1 = HCF(617,1) .

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Frequently Asked Questions on HCF of 840, 529, 617 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 840, 529, 617?

Answer: HCF of 840, 529, 617 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 840, 529, 617 using Euclid's Algorithm?

Answer: For arbitrary numbers 840, 529, 617 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.