Highest Common Factor of 341, 670, 538 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 341, 670, 538 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 341, 670, 538 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 341, 670, 538 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 341, 670, 538 is 1.

HCF(341, 670, 538) = 1

HCF of 341, 670, 538 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 341, 670, 538 is 1.

Highest Common Factor of 341,670,538 using Euclid's algorithm

Highest Common Factor of 341,670,538 is 1

Step 1: Since 670 > 341, we apply the division lemma to 670 and 341, to get

670 = 341 x 1 + 329

Step 2: Since the reminder 341 ≠ 0, we apply division lemma to 329 and 341, to get

341 = 329 x 1 + 12

Step 3: We consider the new divisor 329 and the new remainder 12, and apply the division lemma to get

329 = 12 x 27 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 341 and 670 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(329,12) = HCF(341,329) = HCF(670,341) .

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

Step 1: Since 538 > 1, we apply the division lemma to 538 and 1, to get

538 = 1 x 538 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 538 is 1

Notice that 1 = HCF(538,1) .

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Frequently Asked Questions on HCF of 341, 670, 538 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 341, 670, 538?

Answer: HCF of 341, 670, 538 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 341, 670, 538 using Euclid's Algorithm?

Answer: For arbitrary numbers 341, 670, 538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.