Highest Common Factor of 8654, 1803, 16210 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 8654, 1803, 16210 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8654, 1803, 16210 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 8654, 1803, 16210 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 8654, 1803, 16210 is 1.

HCF(8654, 1803, 16210) = 1

HCF of 8654, 1803, 16210 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 8654, 1803, 16210 is 1.

Highest Common Factor of 8654,1803,16210 using Euclid's algorithm

Highest Common Factor of 8654,1803,16210 is 1

Step 1: Since 8654 > 1803, we apply the division lemma to 8654 and 1803, to get

8654 = 1803 x 4 + 1442

Step 2: Since the reminder 1803 ≠ 0, we apply division lemma to 1442 and 1803, to get

1803 = 1442 x 1 + 361

Step 3: We consider the new divisor 1442 and the new remainder 361, and apply the division lemma to get

1442 = 361 x 3 + 359

We consider the new divisor 361 and the new remainder 359,and apply the division lemma to get

361 = 359 x 1 + 2

We consider the new divisor 359 and the new remainder 2,and apply the division lemma to get

359 = 2 x 179 + 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 8654 and 1803 is 1

Notice that 1 = HCF(2,1) = HCF(359,2) = HCF(361,359) = HCF(1442,361) = HCF(1803,1442) = HCF(8654,1803) .

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

Step 1: Since 16210 > 1, we apply the division lemma to 16210 and 1, to get

16210 = 1 x 16210 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 16210 is 1

Notice that 1 = HCF(16210,1) .

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Frequently Asked Questions on HCF of 8654, 1803, 16210 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 8654, 1803, 16210?

Answer: HCF of 8654, 1803, 16210 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8654, 1803, 16210 using Euclid's Algorithm?

Answer: For arbitrary numbers 8654, 1803, 16210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.