Highest Common Factor of 386, 706, 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 386, 706, 189 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 386, 706, 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 386, 706, 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 386, 706, 189 is 1.

HCF(386, 706, 189) = 1

HCF of 386, 706, 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 386, 706, 189 is 1.

Highest Common Factor of 386,706,189 using Euclid's algorithm

Highest Common Factor of 386,706,189 is 1

Step 1: Since 706 > 386, we apply the division lemma to 706 and 386, to get

706 = 386 x 1 + 320

Step 2: Since the reminder 386 ≠ 0, we apply division lemma to 320 and 386, to get

386 = 320 x 1 + 66

Step 3: We consider the new divisor 320 and the new remainder 66, and apply the division lemma to get

320 = 66 x 4 + 56

We consider the new divisor 66 and the new remainder 56,and apply the division lemma to get

66 = 56 x 1 + 10

We consider the new divisor 56 and the new remainder 10,and apply the division lemma to get

56 = 10 x 5 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 386 and 706 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(56,10) = HCF(66,56) = HCF(320,66) = HCF(386,320) = HCF(706,386) .

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 386, 706, 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 386, 706, 189?

Answer: HCF of 386, 706, 189 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 386, 706, 189 using Euclid's Algorithm?

Answer: For arbitrary numbers 386, 706, 189 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.