Highest Common Factor of 861, 500, 149 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 861, 500, 149 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 861, 500, 149 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 861, 500, 149 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 861, 500, 149 is 1.

HCF(861, 500, 149) = 1

HCF of 861, 500, 149 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 861, 500, 149 is 1.

Highest Common Factor of 861,500,149 using Euclid's algorithm

Highest Common Factor of 861,500,149 is 1

Step 1: Since 861 > 500, we apply the division lemma to 861 and 500, to get

861 = 500 x 1 + 361

Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 361 and 500, to get

500 = 361 x 1 + 139

Step 3: We consider the new divisor 361 and the new remainder 139, and apply the division lemma to get

361 = 139 x 2 + 83

We consider the new divisor 139 and the new remainder 83,and apply the division lemma to get

139 = 83 x 1 + 56

We consider the new divisor 83 and the new remainder 56,and apply the division lemma to get

83 = 56 x 1 + 27

We consider the new divisor 56 and the new remainder 27,and apply the division lemma to get

56 = 27 x 2 + 2

We consider the new divisor 27 and the new remainder 2,and apply the division lemma to get

27 = 2 x 13 + 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 861 and 500 is 1

Notice that 1 = HCF(2,1) = HCF(27,2) = HCF(56,27) = HCF(83,56) = HCF(139,83) = HCF(361,139) = HCF(500,361) = HCF(861,500) .

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

Step 1: Since 149 > 1, we apply the division lemma to 149 and 1, to get

149 = 1 x 149 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 149 is 1

Notice that 1 = HCF(149,1) .

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Frequently Asked Questions on HCF of 861, 500, 149 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 861, 500, 149?

Answer: HCF of 861, 500, 149 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 861, 500, 149 using Euclid's Algorithm?

Answer: For arbitrary numbers 861, 500, 149 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.