Highest Common Factor of 309, 820, 928 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 309, 820, 928 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 309, 820, 928 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 309, 820, 928 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 309, 820, 928 is 1.

HCF(309, 820, 928) = 1

HCF of 309, 820, 928 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 309, 820, 928 is 1.

Highest Common Factor of 309,820,928 using Euclid's algorithm

Highest Common Factor of 309,820,928 is 1

Step 1: Since 820 > 309, we apply the division lemma to 820 and 309, to get

820 = 309 x 2 + 202

Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 202 and 309, to get

309 = 202 x 1 + 107

Step 3: We consider the new divisor 202 and the new remainder 107, and apply the division lemma to get

202 = 107 x 1 + 95

We consider the new divisor 107 and the new remainder 95,and apply the division lemma to get

107 = 95 x 1 + 12

We consider the new divisor 95 and the new remainder 12,and apply the division lemma to get

95 = 12 x 7 + 11

We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get

12 = 11 x 1 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 309 and 820 is 1

Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(95,12) = HCF(107,95) = HCF(202,107) = HCF(309,202) = HCF(820,309) .

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

Step 1: Since 928 > 1, we apply the division lemma to 928 and 1, to get

928 = 1 x 928 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 928 is 1

Notice that 1 = HCF(928,1) .

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Frequently Asked Questions on HCF of 309, 820, 928 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 309, 820, 928?

Answer: HCF of 309, 820, 928 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 309, 820, 928 using Euclid's Algorithm?

Answer: For arbitrary numbers 309, 820, 928 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.