Highest Common Factor of 868, 339, 198 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 868, 339, 198 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 868, 339, 198 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 868, 339, 198 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 868, 339, 198 is 1.

HCF(868, 339, 198) = 1

HCF of 868, 339, 198 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 868, 339, 198 is 1.

Highest Common Factor of 868,339,198 using Euclid's algorithm

Highest Common Factor of 868,339,198 is 1

Step 1: Since 868 > 339, we apply the division lemma to 868 and 339, to get

868 = 339 x 2 + 190

Step 2: Since the reminder 339 ≠ 0, we apply division lemma to 190 and 339, to get

339 = 190 x 1 + 149

Step 3: We consider the new divisor 190 and the new remainder 149, and apply the division lemma to get

190 = 149 x 1 + 41

We consider the new divisor 149 and the new remainder 41,and apply the division lemma to get

149 = 41 x 3 + 26

We consider the new divisor 41 and the new remainder 26,and apply the division lemma to get

41 = 26 x 1 + 15

We consider the new divisor 26 and the new remainder 15,and apply the division lemma to get

26 = 15 x 1 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 868 and 339 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(41,26) = HCF(149,41) = HCF(190,149) = HCF(339,190) = HCF(868,339) .

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

Step 1: Since 198 > 1, we apply the division lemma to 198 and 1, to get

198 = 1 x 198 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 198 is 1

Notice that 1 = HCF(198,1) .

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Frequently Asked Questions on HCF of 868, 339, 198 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 868, 339, 198?

Answer: HCF of 868, 339, 198 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 868, 339, 198 using Euclid's Algorithm?

Answer: For arbitrary numbers 868, 339, 198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.