Highest Common Factor of 861, 542, 613 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, 542, 613 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 861, 542, 613 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, 542, 613 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, 542, 613 is 1.

HCF(861, 542, 613) = 1

HCF of 861, 542, 613 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, 542, 613 is 1.

Highest Common Factor of 861,542,613 using Euclid's algorithm

Highest Common Factor of 861,542,613 is 1

Step 1: Since 861 > 542, we apply the division lemma to 861 and 542, to get

861 = 542 x 1 + 319

Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 319 and 542, to get

542 = 319 x 1 + 223

Step 3: We consider the new divisor 319 and the new remainder 223, and apply the division lemma to get

319 = 223 x 1 + 96

We consider the new divisor 223 and the new remainder 96,and apply the division lemma to get

223 = 96 x 2 + 31

We consider the new divisor 96 and the new remainder 31,and apply the division lemma to get

96 = 31 x 3 + 3

We consider the new divisor 31 and the new remainder 3,and apply the division lemma to get

31 = 3 x 10 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 861 and 542 is 1

Notice that 1 = HCF(3,1) = HCF(31,3) = HCF(96,31) = HCF(223,96) = HCF(319,223) = HCF(542,319) = HCF(861,542) .

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

Step 1: Since 613 > 1, we apply the division lemma to 613 and 1, to get

613 = 1 x 613 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 613 is 1

Notice that 1 = HCF(613,1) .

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Frequently Asked Questions on HCF of 861, 542, 613 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, 542, 613?

Answer: HCF of 861, 542, 613 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 861, 542, 613 using Euclid's Algorithm?

Answer: For arbitrary numbers 861, 542, 613 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.