Highest Common Factor of 838, 174, 189 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 838, 174, 189 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 838, 174, 189 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 838, 174, 189 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 838, 174, 189 is 1.

HCF(838, 174, 189) = 1

HCF of 838, 174, 189 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 838, 174, 189 is 1.

Highest Common Factor of 838,174,189 using Euclid's algorithm

Highest Common Factor of 838,174,189 is 1

Step 1: Since 838 > 174, we apply the division lemma to 838 and 174, to get

838 = 174 x 4 + 142

Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 142 and 174, to get

174 = 142 x 1 + 32

Step 3: We consider the new divisor 142 and the new remainder 32, and apply the division lemma to get

142 = 32 x 4 + 14

We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get

32 = 14 x 2 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 838 and 174 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(142,32) = HCF(174,142) = HCF(838,174) .

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

Step 1: Since 189 > 2, we apply the division lemma to 189 and 2, to get

189 = 2 x 94 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 189 is 1

Notice that 1 = HCF(2,1) = HCF(189,2) .

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Frequently Asked Questions on HCF of 838, 174, 189 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 838, 174, 189?

Answer: HCF of 838, 174, 189 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 838, 174, 189 using Euclid's Algorithm?

Answer: For arbitrary numbers 838, 174, 189 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.