Highest Common Factor of 328, 9687, 2024 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 328, 9687, 2024 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 328, 9687, 2024 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 328, 9687, 2024 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 328, 9687, 2024 is 1.

HCF(328, 9687, 2024) = 1

HCF of 328, 9687, 2024 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 328, 9687, 2024 is 1.

Highest Common Factor of 328,9687,2024 using Euclid's algorithm

Highest Common Factor of 328,9687,2024 is 1

Step 1: Since 9687 > 328, we apply the division lemma to 9687 and 328, to get

9687 = 328 x 29 + 175

Step 2: Since the reminder 328 ≠ 0, we apply division lemma to 175 and 328, to get

328 = 175 x 1 + 153

Step 3: We consider the new divisor 175 and the new remainder 153, and apply the division lemma to get

175 = 153 x 1 + 22

We consider the new divisor 153 and the new remainder 22,and apply the division lemma to get

153 = 22 x 6 + 21

We consider the new divisor 22 and the new remainder 21,and apply the division lemma to get

22 = 21 x 1 + 1

We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get

21 = 1 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 328 and 9687 is 1

Notice that 1 = HCF(21,1) = HCF(22,21) = HCF(153,22) = HCF(175,153) = HCF(328,175) = HCF(9687,328) .

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

Step 1: Since 2024 > 1, we apply the division lemma to 2024 and 1, to get

2024 = 1 x 2024 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2024 is 1

Notice that 1 = HCF(2024,1) .

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Frequently Asked Questions on HCF of 328, 9687, 2024 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 328, 9687, 2024?

Answer: HCF of 328, 9687, 2024 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 328, 9687, 2024 using Euclid's Algorithm?

Answer: For arbitrary numbers 328, 9687, 2024 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.