Highest Common Factor of 822, 605, 146 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 822, 605, 146 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 822, 605, 146 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 822, 605, 146 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 822, 605, 146 is 1.

HCF(822, 605, 146) = 1

HCF of 822, 605, 146 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 822, 605, 146 is 1.

Highest Common Factor of 822,605,146 using Euclid's algorithm

Highest Common Factor of 822,605,146 is 1

Step 1: Since 822 > 605, we apply the division lemma to 822 and 605, to get

822 = 605 x 1 + 217

Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 217 and 605, to get

605 = 217 x 2 + 171

Step 3: We consider the new divisor 217 and the new remainder 171, and apply the division lemma to get

217 = 171 x 1 + 46

We consider the new divisor 171 and the new remainder 46,and apply the division lemma to get

171 = 46 x 3 + 33

We consider the new divisor 46 and the new remainder 33,and apply the division lemma to get

46 = 33 x 1 + 13

We consider the new divisor 33 and the new remainder 13,and apply the division lemma to get

33 = 13 x 2 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 822 and 605 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(33,13) = HCF(46,33) = HCF(171,46) = HCF(217,171) = HCF(605,217) = HCF(822,605) .

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

Step 1: Since 146 > 1, we apply the division lemma to 146 and 1, to get

146 = 1 x 146 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 146 is 1

Notice that 1 = HCF(146,1) .

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Frequently Asked Questions on HCF of 822, 605, 146 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 822, 605, 146?

Answer: HCF of 822, 605, 146 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 822, 605, 146 using Euclid's Algorithm?

Answer: For arbitrary numbers 822, 605, 146 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.