Highest Common Factor of 841, 614, 84 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 841, 614, 84 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 841, 614, 84 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 841, 614, 84 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 841, 614, 84 is 1.

HCF(841, 614, 84) = 1

HCF of 841, 614, 84 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 841, 614, 84 is 1.

Highest Common Factor of 841,614,84 using Euclid's algorithm

Highest Common Factor of 841,614,84 is 1

Step 1: Since 841 > 614, we apply the division lemma to 841 and 614, to get

841 = 614 x 1 + 227

Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 227 and 614, to get

614 = 227 x 2 + 160

Step 3: We consider the new divisor 227 and the new remainder 160, and apply the division lemma to get

227 = 160 x 1 + 67

We consider the new divisor 160 and the new remainder 67,and apply the division lemma to get

160 = 67 x 2 + 26

We consider the new divisor 67 and the new remainder 26,and apply the division lemma to get

67 = 26 x 2 + 15

We consider the new divisor 26 and the new remainder 15,and apply the division lemma to get

26 = 15 x 1 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

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

4 = 3 x 1 + 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 841 and 614 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(67,26) = HCF(160,67) = HCF(227,160) = HCF(614,227) = HCF(841,614) .

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

Step 1: Since 84 > 1, we apply the division lemma to 84 and 1, to get

84 = 1 x 84 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 84 is 1

Notice that 1 = HCF(84,1) .

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Frequently Asked Questions on HCF of 841, 614, 84 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 841, 614, 84?

Answer: HCF of 841, 614, 84 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 841, 614, 84 using Euclid's Algorithm?

Answer: For arbitrary numbers 841, 614, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.