Highest Common Factor of 921, 605, 892 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 921, 605, 892 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 921, 605, 892 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 921, 605, 892 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 921, 605, 892 is 1.

HCF(921, 605, 892) = 1

HCF of 921, 605, 892 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 921, 605, 892 is 1.

Highest Common Factor of 921,605,892 using Euclid's algorithm

Highest Common Factor of 921,605,892 is 1

Step 1: Since 921 > 605, we apply the division lemma to 921 and 605, to get

921 = 605 x 1 + 316

Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 316 and 605, to get

605 = 316 x 1 + 289

Step 3: We consider the new divisor 316 and the new remainder 289, and apply the division lemma to get

316 = 289 x 1 + 27

We consider the new divisor 289 and the new remainder 27,and apply the division lemma to get

289 = 27 x 10 + 19

We consider the new divisor 27 and the new remainder 19,and apply the division lemma to get

27 = 19 x 1 + 8

We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get

19 = 8 x 2 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

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

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 921 and 605 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(289,27) = HCF(316,289) = HCF(605,316) = HCF(921,605) .

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

Step 1: Since 892 > 1, we apply the division lemma to 892 and 1, to get

892 = 1 x 892 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 892 is 1

Notice that 1 = HCF(892,1) .

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Frequently Asked Questions on HCF of 921, 605, 892 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 921, 605, 892?

Answer: HCF of 921, 605, 892 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 921, 605, 892 using Euclid's Algorithm?

Answer: For arbitrary numbers 921, 605, 892 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.