Highest Common Factor of 338, 542, 805 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 338, 542, 805 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 338, 542, 805 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 338, 542, 805 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 338, 542, 805 is 1.

HCF(338, 542, 805) = 1

HCF of 338, 542, 805 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 338, 542, 805 is 1.

Highest Common Factor of 338,542,805 using Euclid's algorithm

Highest Common Factor of 338,542,805 is 1

Step 1: Since 542 > 338, we apply the division lemma to 542 and 338, to get

542 = 338 x 1 + 204

Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 204 and 338, to get

338 = 204 x 1 + 134

Step 3: We consider the new divisor 204 and the new remainder 134, and apply the division lemma to get

204 = 134 x 1 + 70

We consider the new divisor 134 and the new remainder 70,and apply the division lemma to get

134 = 70 x 1 + 64

We consider the new divisor 70 and the new remainder 64,and apply the division lemma to get

70 = 64 x 1 + 6

We consider the new divisor 64 and the new remainder 6,and apply the division lemma to get

64 = 6 x 10 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 338 and 542 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(64,6) = HCF(70,64) = HCF(134,70) = HCF(204,134) = HCF(338,204) = HCF(542,338) .

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

Step 1: Since 805 > 2, we apply the division lemma to 805 and 2, to get

805 = 2 x 402 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 805 is 1

Notice that 1 = HCF(2,1) = HCF(805,2) .

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Frequently Asked Questions on HCF of 338, 542, 805 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 338, 542, 805?

Answer: HCF of 338, 542, 805 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 338, 542, 805 using Euclid's Algorithm?

Answer: For arbitrary numbers 338, 542, 805 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.