Highest Common Factor of 842, 2040, 8621 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 842, 2040, 8621 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 842, 2040, 8621 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 842, 2040, 8621 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 842, 2040, 8621 is 1.

HCF(842, 2040, 8621) = 1

HCF of 842, 2040, 8621 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 842, 2040, 8621 is 1.

Highest Common Factor of 842,2040,8621 using Euclid's algorithm

Highest Common Factor of 842,2040,8621 is 1

Step 1: Since 2040 > 842, we apply the division lemma to 2040 and 842, to get

2040 = 842 x 2 + 356

Step 2: Since the reminder 842 ≠ 0, we apply division lemma to 356 and 842, to get

842 = 356 x 2 + 130

Step 3: We consider the new divisor 356 and the new remainder 130, and apply the division lemma to get

356 = 130 x 2 + 96

We consider the new divisor 130 and the new remainder 96,and apply the division lemma to get

130 = 96 x 1 + 34

We consider the new divisor 96 and the new remainder 34,and apply the division lemma to get

96 = 34 x 2 + 28

We consider the new divisor 34 and the new remainder 28,and apply the division lemma to get

34 = 28 x 1 + 6

We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get

28 = 6 x 4 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

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 842 and 2040 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(96,34) = HCF(130,96) = HCF(356,130) = HCF(842,356) = HCF(2040,842) .

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

Step 1: Since 8621 > 2, we apply the division lemma to 8621 and 2, to get

8621 = 2 x 4310 + 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 8621 is 1

Notice that 1 = HCF(2,1) = HCF(8621,2) .

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Frequently Asked Questions on HCF of 842, 2040, 8621 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 842, 2040, 8621?

Answer: HCF of 842, 2040, 8621 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 842, 2040, 8621 using Euclid's Algorithm?

Answer: For arbitrary numbers 842, 2040, 8621 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.