Highest Common Factor of 337, 574, 334 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 337, 574, 334 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 337, 574, 334 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 337, 574, 334 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 337, 574, 334 is 1.

HCF(337, 574, 334) = 1

HCF of 337, 574, 334 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 337, 574, 334 is 1.

Highest Common Factor of 337,574,334 using Euclid's algorithm

Highest Common Factor of 337,574,334 is 1

Step 1: Since 574 > 337, we apply the division lemma to 574 and 337, to get

574 = 337 x 1 + 237

Step 2: Since the reminder 337 ≠ 0, we apply division lemma to 237 and 337, to get

337 = 237 x 1 + 100

Step 3: We consider the new divisor 237 and the new remainder 100, and apply the division lemma to get

237 = 100 x 2 + 37

We consider the new divisor 100 and the new remainder 37,and apply the division lemma to get

100 = 37 x 2 + 26

We consider the new divisor 37 and the new remainder 26,and apply the division lemma to get

37 = 26 x 1 + 11

We consider the new divisor 26 and the new remainder 11,and apply the division lemma to get

26 = 11 x 2 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

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

4 = 3 x 1 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 337 and 574 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(26,11) = HCF(37,26) = HCF(100,37) = HCF(237,100) = HCF(337,237) = HCF(574,337) .

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

Step 1: Since 334 > 1, we apply the division lemma to 334 and 1, to get

334 = 1 x 334 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 334 is 1

Notice that 1 = HCF(334,1) .

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Frequently Asked Questions on HCF of 337, 574, 334 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 337, 574, 334?

Answer: HCF of 337, 574, 334 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 337, 574, 334 using Euclid's Algorithm?

Answer: For arbitrary numbers 337, 574, 334 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.