Highest Common Factor of 398, 9000, 1571 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 398, 9000, 1571 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 398, 9000, 1571 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 398, 9000, 1571 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 398, 9000, 1571 is 1.

HCF(398, 9000, 1571) = 1

HCF of 398, 9000, 1571 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 398, 9000, 1571 is 1.

Highest Common Factor of 398,9000,1571 using Euclid's algorithm

Highest Common Factor of 398,9000,1571 is 1

Step 1: Since 9000 > 398, we apply the division lemma to 9000 and 398, to get

9000 = 398 x 22 + 244

Step 2: Since the reminder 398 ≠ 0, we apply division lemma to 244 and 398, to get

398 = 244 x 1 + 154

Step 3: We consider the new divisor 244 and the new remainder 154, and apply the division lemma to get

244 = 154 x 1 + 90

We consider the new divisor 154 and the new remainder 90,and apply the division lemma to get

154 = 90 x 1 + 64

We consider the new divisor 90 and the new remainder 64,and apply the division lemma to get

90 = 64 x 1 + 26

We consider the new divisor 64 and the new remainder 26,and apply the division lemma to get

64 = 26 x 2 + 12

We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get

26 = 12 x 2 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 398 and 9000 is 2

Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(64,26) = HCF(90,64) = HCF(154,90) = HCF(244,154) = HCF(398,244) = HCF(9000,398) .

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

Step 1: Since 1571 > 2, we apply the division lemma to 1571 and 2, to get

1571 = 2 x 785 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 1571 is 1

Notice that 1 = HCF(2,1) = HCF(1571,2) .

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Frequently Asked Questions on HCF of 398, 9000, 1571 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 398, 9000, 1571?

Answer: HCF of 398, 9000, 1571 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 398, 9000, 1571 using Euclid's Algorithm?

Answer: For arbitrary numbers 398, 9000, 1571 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.