Highest Common Factor of 805, 515, 314 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 805, 515, 314 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 805, 515, 314 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 805, 515, 314 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 805, 515, 314 is 1.

HCF(805, 515, 314) = 1

HCF of 805, 515, 314 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 805, 515, 314 is 1.

Highest Common Factor of 805,515,314 using Euclid's algorithm

Highest Common Factor of 805,515,314 is 1

Step 1: Since 805 > 515, we apply the division lemma to 805 and 515, to get

805 = 515 x 1 + 290

Step 2: Since the reminder 515 ≠ 0, we apply division lemma to 290 and 515, to get

515 = 290 x 1 + 225

Step 3: We consider the new divisor 290 and the new remainder 225, and apply the division lemma to get

290 = 225 x 1 + 65

We consider the new divisor 225 and the new remainder 65,and apply the division lemma to get

225 = 65 x 3 + 30

We consider the new divisor 65 and the new remainder 30,and apply the division lemma to get

65 = 30 x 2 + 5

We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get

30 = 5 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 805 and 515 is 5

Notice that 5 = HCF(30,5) = HCF(65,30) = HCF(225,65) = HCF(290,225) = HCF(515,290) = HCF(805,515) .

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

Step 1: Since 314 > 5, we apply the division lemma to 314 and 5, to get

314 = 5 x 62 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 314 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(314,5) .

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Frequently Asked Questions on HCF of 805, 515, 314 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 805, 515, 314?

Answer: HCF of 805, 515, 314 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 805, 515, 314 using Euclid's Algorithm?

Answer: For arbitrary numbers 805, 515, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.