Highest Common Factor of 705, 610, 386 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 705, 610, 386 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 705, 610, 386 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 705, 610, 386 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 705, 610, 386 is 1.

HCF(705, 610, 386) = 1

HCF of 705, 610, 386 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 705, 610, 386 is 1.

Highest Common Factor of 705,610,386 using Euclid's algorithm

Highest Common Factor of 705,610,386 is 1

Step 1: Since 705 > 610, we apply the division lemma to 705 and 610, to get

705 = 610 x 1 + 95

Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 95 and 610, to get

610 = 95 x 6 + 40

Step 3: We consider the new divisor 95 and the new remainder 40, and apply the division lemma to get

95 = 40 x 2 + 15

We consider the new divisor 40 and the new remainder 15,and apply the division lemma to get

40 = 15 x 2 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 705 and 610 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(95,40) = HCF(610,95) = HCF(705,610) .

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

Step 1: Since 386 > 5, we apply the division lemma to 386 and 5, to get

386 = 5 x 77 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 386 is 1

Notice that 1 = HCF(5,1) = HCF(386,5) .

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Frequently Asked Questions on HCF of 705, 610, 386 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 705, 610, 386?

Answer: HCF of 705, 610, 386 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 705, 610, 386 using Euclid's Algorithm?

Answer: For arbitrary numbers 705, 610, 386 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.