Highest Common Factor of 706, 8005, 2815 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 706, 8005, 2815 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 706, 8005, 2815 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 706, 8005, 2815 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 706, 8005, 2815 is 1.

HCF(706, 8005, 2815) = 1

HCF of 706, 8005, 2815 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 706, 8005, 2815 is 1.

Highest Common Factor of 706,8005,2815 using Euclid's algorithm

Highest Common Factor of 706,8005,2815 is 1

Step 1: Since 8005 > 706, we apply the division lemma to 8005 and 706, to get

8005 = 706 x 11 + 239

Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 239 and 706, to get

706 = 239 x 2 + 228

Step 3: We consider the new divisor 239 and the new remainder 228, and apply the division lemma to get

239 = 228 x 1 + 11

We consider the new divisor 228 and the new remainder 11,and apply the division lemma to get

228 = 11 x 20 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 706 and 8005 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(228,11) = HCF(239,228) = HCF(706,239) = HCF(8005,706) .

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

Step 1: Since 2815 > 1, we apply the division lemma to 2815 and 1, to get

2815 = 1 x 2815 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2815 is 1

Notice that 1 = HCF(2815,1) .

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Frequently Asked Questions on HCF of 706, 8005, 2815 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 706, 8005, 2815?

Answer: HCF of 706, 8005, 2815 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 706, 8005, 2815 using Euclid's Algorithm?

Answer: For arbitrary numbers 706, 8005, 2815 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.