Highest Common Factor of 689, 353, 868 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 689, 353, 868 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 689, 353, 868 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 689, 353, 868 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 689, 353, 868 is 1.

HCF(689, 353, 868) = 1

HCF of 689, 353, 868 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 689, 353, 868 is 1.

Highest Common Factor of 689,353,868 using Euclid's algorithm

Highest Common Factor of 689,353,868 is 1

Step 1: Since 689 > 353, we apply the division lemma to 689 and 353, to get

689 = 353 x 1 + 336

Step 2: Since the reminder 353 ≠ 0, we apply division lemma to 336 and 353, to get

353 = 336 x 1 + 17

Step 3: We consider the new divisor 336 and the new remainder 17, and apply the division lemma to get

336 = 17 x 19 + 13

We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get

17 = 13 x 1 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 689 and 353 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(336,17) = HCF(353,336) = HCF(689,353) .

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

Step 1: Since 868 > 1, we apply the division lemma to 868 and 1, to get

868 = 1 x 868 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 868 is 1

Notice that 1 = HCF(868,1) .

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Frequently Asked Questions on HCF of 689, 353, 868 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 689, 353, 868?

Answer: HCF of 689, 353, 868 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 689, 353, 868 using Euclid's Algorithm?

Answer: For arbitrary numbers 689, 353, 868 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.