Highest Common Factor of 820, 232, 382 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 820, 232, 382 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 820, 232, 382 is 2 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 820, 232, 382 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 820, 232, 382 is 2.

HCF(820, 232, 382) = 2

HCF of 820, 232, 382 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 820, 232, 382 is 2.

Highest Common Factor of 820,232,382 using Euclid's algorithm

Highest Common Factor of 820,232,382 is 2

Step 1: Since 820 > 232, we apply the division lemma to 820 and 232, to get

820 = 232 x 3 + 124

Step 2: Since the reminder 232 ≠ 0, we apply division lemma to 124 and 232, to get

232 = 124 x 1 + 108

Step 3: We consider the new divisor 124 and the new remainder 108, and apply the division lemma to get

124 = 108 x 1 + 16

We consider the new divisor 108 and the new remainder 16,and apply the division lemma to get

108 = 16 x 6 + 12

We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get

16 = 12 x 1 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 820 and 232 is 4

Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(108,16) = HCF(124,108) = HCF(232,124) = HCF(820,232) .

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

Step 1: Since 382 > 4, we apply the division lemma to 382 and 4, to get

382 = 4 x 95 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 382 is 2

Notice that 2 = HCF(4,2) = HCF(382,4) .

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Frequently Asked Questions on HCF of 820, 232, 382 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 820, 232, 382?

Answer: HCF of 820, 232, 382 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 820, 232, 382 using Euclid's Algorithm?

Answer: For arbitrary numbers 820, 232, 382 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.