Highest Common Factor of 523, 3646, 9198 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 523, 3646, 9198 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 523, 3646, 9198 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 523, 3646, 9198 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 523, 3646, 9198 is 1.

HCF(523, 3646, 9198) = 1

HCF of 523, 3646, 9198 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 523, 3646, 9198 is 1.

Highest Common Factor of 523,3646,9198 using Euclid's algorithm

Highest Common Factor of 523,3646,9198 is 1

Step 1: Since 3646 > 523, we apply the division lemma to 3646 and 523, to get

3646 = 523 x 6 + 508

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 508 and 523, to get

523 = 508 x 1 + 15

Step 3: We consider the new divisor 508 and the new remainder 15, and apply the division lemma to get

508 = 15 x 33 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 523 and 3646 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(508,15) = HCF(523,508) = HCF(3646,523) .

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

Step 1: Since 9198 > 1, we apply the division lemma to 9198 and 1, to get

9198 = 1 x 9198 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9198 is 1

Notice that 1 = HCF(9198,1) .

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Frequently Asked Questions on HCF of 523, 3646, 9198 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 523, 3646, 9198?

Answer: HCF of 523, 3646, 9198 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 523, 3646, 9198 using Euclid's Algorithm?

Answer: For arbitrary numbers 523, 3646, 9198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.