Highest Common Factor of 815, 639, 354 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 815, 639, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 815, 639, 354 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 815, 639, 354 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 815, 639, 354 is 1.

HCF(815, 639, 354) = 1

HCF of 815, 639, 354 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 815, 639, 354 is 1.

Highest Common Factor of 815,639,354 using Euclid's algorithm

Highest Common Factor of 815,639,354 is 1

Step 1: Since 815 > 639, we apply the division lemma to 815 and 639, to get

815 = 639 x 1 + 176

Step 2: Since the reminder 639 ≠ 0, we apply division lemma to 176 and 639, to get

639 = 176 x 3 + 111

Step 3: We consider the new divisor 176 and the new remainder 111, and apply the division lemma to get

176 = 111 x 1 + 65

We consider the new divisor 111 and the new remainder 65,and apply the division lemma to get

111 = 65 x 1 + 46

We consider the new divisor 65 and the new remainder 46,and apply the division lemma to get

65 = 46 x 1 + 19

We consider the new divisor 46 and the new remainder 19,and apply the division lemma to get

46 = 19 x 2 + 8

We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get

19 = 8 x 2 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 815 and 639 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(46,19) = HCF(65,46) = HCF(111,65) = HCF(176,111) = HCF(639,176) = HCF(815,639) .

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

Step 1: Since 354 > 1, we apply the division lemma to 354 and 1, to get

354 = 1 x 354 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 354 is 1

Notice that 1 = HCF(354,1) .

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Frequently Asked Questions on HCF of 815, 639, 354 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 815, 639, 354?

Answer: HCF of 815, 639, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 815, 639, 354 using Euclid's Algorithm?

Answer: For arbitrary numbers 815, 639, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.