Highest Common Factor of 866, 487, 345 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 866, 487, 345 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 866, 487, 345 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 866, 487, 345 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 866, 487, 345 is 1.

HCF(866, 487, 345) = 1

HCF of 866, 487, 345 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 866, 487, 345 is 1.

Highest Common Factor of 866,487,345 using Euclid's algorithm

Highest Common Factor of 866,487,345 is 1

Step 1: Since 866 > 487, we apply the division lemma to 866 and 487, to get

866 = 487 x 1 + 379

Step 2: Since the reminder 487 ≠ 0, we apply division lemma to 379 and 487, to get

487 = 379 x 1 + 108

Step 3: We consider the new divisor 379 and the new remainder 108, and apply the division lemma to get

379 = 108 x 3 + 55

We consider the new divisor 108 and the new remainder 55,and apply the division lemma to get

108 = 55 x 1 + 53

We consider the new divisor 55 and the new remainder 53,and apply the division lemma to get

55 = 53 x 1 + 2

We consider the new divisor 53 and the new remainder 2,and apply the division lemma to get

53 = 2 x 26 + 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 866 and 487 is 1

Notice that 1 = HCF(2,1) = HCF(53,2) = HCF(55,53) = HCF(108,55) = HCF(379,108) = HCF(487,379) = HCF(866,487) .

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

Step 1: Since 345 > 1, we apply the division lemma to 345 and 1, to get

345 = 1 x 345 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 345 is 1

Notice that 1 = HCF(345,1) .

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Frequently Asked Questions on HCF of 866, 487, 345 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 866, 487, 345?

Answer: HCF of 866, 487, 345 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 866, 487, 345 using Euclid's Algorithm?

Answer: For arbitrary numbers 866, 487, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.