Highest Common Factor of 2087, 1866, 34770 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 2087, 1866, 34770 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2087, 1866, 34770 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 2087, 1866, 34770 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 2087, 1866, 34770 is 1.

HCF(2087, 1866, 34770) = 1

HCF of 2087, 1866, 34770 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 2087, 1866, 34770 is 1.

Highest Common Factor of 2087,1866,34770 using Euclid's algorithm

Highest Common Factor of 2087,1866,34770 is 1

Step 1: Since 2087 > 1866, we apply the division lemma to 2087 and 1866, to get

2087 = 1866 x 1 + 221

Step 2: Since the reminder 1866 ≠ 0, we apply division lemma to 221 and 1866, to get

1866 = 221 x 8 + 98

Step 3: We consider the new divisor 221 and the new remainder 98, and apply the division lemma to get

221 = 98 x 2 + 25

We consider the new divisor 98 and the new remainder 25,and apply the division lemma to get

98 = 25 x 3 + 23

We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get

25 = 23 x 1 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 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 2087 and 1866 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(98,25) = HCF(221,98) = HCF(1866,221) = HCF(2087,1866) .

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

Step 1: Since 34770 > 1, we apply the division lemma to 34770 and 1, to get

34770 = 1 x 34770 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 34770 is 1

Notice that 1 = HCF(34770,1) .

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Frequently Asked Questions on HCF of 2087, 1866, 34770 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 2087, 1866, 34770?

Answer: HCF of 2087, 1866, 34770 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2087, 1866, 34770 using Euclid's Algorithm?

Answer: For arbitrary numbers 2087, 1866, 34770 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.