Highest Common Factor of 814, 369, 176 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 814, 369, 176 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 814, 369, 176 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 814, 369, 176 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 814, 369, 176 is 1.

HCF(814, 369, 176) = 1

HCF of 814, 369, 176 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 814, 369, 176 is 1.

Highest Common Factor of 814,369,176 using Euclid's algorithm

Highest Common Factor of 814,369,176 is 1

Step 1: Since 814 > 369, we apply the division lemma to 814 and 369, to get

814 = 369 x 2 + 76

Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 76 and 369, to get

369 = 76 x 4 + 65

Step 3: We consider the new divisor 76 and the new remainder 65, and apply the division lemma to get

76 = 65 x 1 + 11

We consider the new divisor 65 and the new remainder 11,and apply the division lemma to get

65 = 11 x 5 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 814 and 369 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(65,11) = HCF(76,65) = HCF(369,76) = HCF(814,369) .

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

Step 1: Since 176 > 1, we apply the division lemma to 176 and 1, to get

176 = 1 x 176 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 176 is 1

Notice that 1 = HCF(176,1) .

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Frequently Asked Questions on HCF of 814, 369, 176 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 814, 369, 176?

Answer: HCF of 814, 369, 176 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 814, 369, 176 using Euclid's Algorithm?

Answer: For arbitrary numbers 814, 369, 176 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.