Highest Common Factor of 186, 720, 820, 641 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 186, 720, 820, 641 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 186, 720, 820, 641 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 186, 720, 820, 641 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 186, 720, 820, 641 is 1.

HCF(186, 720, 820, 641) = 1

HCF of 186, 720, 820, 641 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 186, 720, 820, 641 is 1.

Highest Common Factor of 186,720,820,641 using Euclid's algorithm

Highest Common Factor of 186,720,820,641 is 1

Step 1: Since 720 > 186, we apply the division lemma to 720 and 186, to get

720 = 186 x 3 + 162

Step 2: Since the reminder 186 ≠ 0, we apply division lemma to 162 and 186, to get

186 = 162 x 1 + 24

Step 3: We consider the new divisor 162 and the new remainder 24, and apply the division lemma to get

162 = 24 x 6 + 18

We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get

24 = 18 x 1 + 6

We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get

18 = 6 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 186 and 720 is 6

Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(162,24) = HCF(186,162) = HCF(720,186) .

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

Step 1: Since 820 > 6, we apply the division lemma to 820 and 6, to get

820 = 6 x 136 + 4

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get

6 = 4 x 1 + 2

Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 820 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(820,6) .

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

Step 1: Since 641 > 2, we apply the division lemma to 641 and 2, to get

641 = 2 x 320 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 641 is 1

Notice that 1 = HCF(2,1) = HCF(641,2) .

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Frequently Asked Questions on HCF of 186, 720, 820, 641 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 186, 720, 820, 641?

Answer: HCF of 186, 720, 820, 641 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 186, 720, 820, 641 using Euclid's Algorithm?

Answer: For arbitrary numbers 186, 720, 820, 641 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.