Highest Common Factor of 8118, 4973, 32000 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 8118, 4973, 32000 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8118, 4973, 32000 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 8118, 4973, 32000 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 8118, 4973, 32000 is 1.

HCF(8118, 4973, 32000) = 1

HCF of 8118, 4973, 32000 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 8118, 4973, 32000 is 1.

Highest Common Factor of 8118,4973,32000 using Euclid's algorithm

Highest Common Factor of 8118,4973,32000 is 1

Step 1: Since 8118 > 4973, we apply the division lemma to 8118 and 4973, to get

8118 = 4973 x 1 + 3145

Step 2: Since the reminder 4973 ≠ 0, we apply division lemma to 3145 and 4973, to get

4973 = 3145 x 1 + 1828

Step 3: We consider the new divisor 3145 and the new remainder 1828, and apply the division lemma to get

3145 = 1828 x 1 + 1317

We consider the new divisor 1828 and the new remainder 1317,and apply the division lemma to get

1828 = 1317 x 1 + 511

We consider the new divisor 1317 and the new remainder 511,and apply the division lemma to get

1317 = 511 x 2 + 295

We consider the new divisor 511 and the new remainder 295,and apply the division lemma to get

511 = 295 x 1 + 216

We consider the new divisor 295 and the new remainder 216,and apply the division lemma to get

295 = 216 x 1 + 79

We consider the new divisor 216 and the new remainder 79,and apply the division lemma to get

216 = 79 x 2 + 58

We consider the new divisor 79 and the new remainder 58,and apply the division lemma to get

79 = 58 x 1 + 21

We consider the new divisor 58 and the new remainder 21,and apply the division lemma to get

58 = 21 x 2 + 16

We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get

21 = 16 x 1 + 5

We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get

16 = 5 x 3 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8118 and 4973 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(58,21) = HCF(79,58) = HCF(216,79) = HCF(295,216) = HCF(511,295) = HCF(1317,511) = HCF(1828,1317) = HCF(3145,1828) = HCF(4973,3145) = HCF(8118,4973) .

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

Step 1: Since 32000 > 1, we apply the division lemma to 32000 and 1, to get

32000 = 1 x 32000 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32000 is 1

Notice that 1 = HCF(32000,1) .

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Frequently Asked Questions on HCF of 8118, 4973, 32000 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 8118, 4973, 32000?

Answer: HCF of 8118, 4973, 32000 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8118, 4973, 32000 using Euclid's Algorithm?

Answer: For arbitrary numbers 8118, 4973, 32000 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.