Highest Common Factor of 1023, 8422, 72906 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 1023, 8422, 72906 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1023, 8422, 72906 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 1023, 8422, 72906 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 1023, 8422, 72906 is 1.

HCF(1023, 8422, 72906) = 1

HCF of 1023, 8422, 72906 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 1023, 8422, 72906 is 1.

Highest Common Factor of 1023,8422,72906 using Euclid's algorithm

Highest Common Factor of 1023,8422,72906 is 1

Step 1: Since 8422 > 1023, we apply the division lemma to 8422 and 1023, to get

8422 = 1023 x 8 + 238

Step 2: Since the reminder 1023 ≠ 0, we apply division lemma to 238 and 1023, to get

1023 = 238 x 4 + 71

Step 3: We consider the new divisor 238 and the new remainder 71, and apply the division lemma to get

238 = 71 x 3 + 25

We consider the new divisor 71 and the new remainder 25,and apply the division lemma to get

71 = 25 x 2 + 21

We consider the new divisor 25 and the new remainder 21,and apply the division lemma to get

25 = 21 x 1 + 4

We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get

21 = 4 x 5 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1023 and 8422 is 1

Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(25,21) = HCF(71,25) = HCF(238,71) = HCF(1023,238) = HCF(8422,1023) .

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

Step 1: Since 72906 > 1, we apply the division lemma to 72906 and 1, to get

72906 = 1 x 72906 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 72906 is 1

Notice that 1 = HCF(72906,1) .

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Frequently Asked Questions on HCF of 1023, 8422, 72906 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 1023, 8422, 72906?

Answer: HCF of 1023, 8422, 72906 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1023, 8422, 72906 using Euclid's Algorithm?

Answer: For arbitrary numbers 1023, 8422, 72906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.