Highest Common Factor of 865, 677, 182 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 865, 677, 182 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 865, 677, 182 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 865, 677, 182 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 865, 677, 182 is 1.

HCF(865, 677, 182) = 1

HCF of 865, 677, 182 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 865, 677, 182 is 1.

Highest Common Factor of 865,677,182 using Euclid's algorithm

Highest Common Factor of 865,677,182 is 1

Step 1: Since 865 > 677, we apply the division lemma to 865 and 677, to get

865 = 677 x 1 + 188

Step 2: Since the reminder 677 ≠ 0, we apply division lemma to 188 and 677, to get

677 = 188 x 3 + 113

Step 3: We consider the new divisor 188 and the new remainder 113, and apply the division lemma to get

188 = 113 x 1 + 75

We consider the new divisor 113 and the new remainder 75,and apply the division lemma to get

113 = 75 x 1 + 38

We consider the new divisor 75 and the new remainder 38,and apply the division lemma to get

75 = 38 x 1 + 37

We consider the new divisor 38 and the new remainder 37,and apply the division lemma to get

38 = 37 x 1 + 1

We consider the new divisor 37 and the new remainder 1,and apply the division lemma to get

37 = 1 x 37 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 865 and 677 is 1

Notice that 1 = HCF(37,1) = HCF(38,37) = HCF(75,38) = HCF(113,75) = HCF(188,113) = HCF(677,188) = HCF(865,677) .

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

Step 1: Since 182 > 1, we apply the division lemma to 182 and 1, to get

182 = 1 x 182 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 182 is 1

Notice that 1 = HCF(182,1) .

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Frequently Asked Questions on HCF of 865, 677, 182 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 865, 677, 182?

Answer: HCF of 865, 677, 182 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 865, 677, 182 using Euclid's Algorithm?

Answer: For arbitrary numbers 865, 677, 182 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.