Highest Common Factor of 336, 514, 423 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 336, 514, 423 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 336, 514, 423 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 336, 514, 423 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 336, 514, 423 is 1.

HCF(336, 514, 423) = 1

HCF of 336, 514, 423 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 336, 514, 423 is 1.

Highest Common Factor of 336,514,423 using Euclid's algorithm

Highest Common Factor of 336,514,423 is 1

Step 1: Since 514 > 336, we apply the division lemma to 514 and 336, to get

514 = 336 x 1 + 178

Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 178 and 336, to get

336 = 178 x 1 + 158

Step 3: We consider the new divisor 178 and the new remainder 158, and apply the division lemma to get

178 = 158 x 1 + 20

We consider the new divisor 158 and the new remainder 20,and apply the division lemma to get

158 = 20 x 7 + 18

We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get

20 = 18 x 1 + 2

We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get

18 = 2 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 336 and 514 is 2

Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(158,20) = HCF(178,158) = HCF(336,178) = HCF(514,336) .

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

Step 1: Since 423 > 2, we apply the division lemma to 423 and 2, to get

423 = 2 x 211 + 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 423 is 1

Notice that 1 = HCF(2,1) = HCF(423,2) .

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Frequently Asked Questions on HCF of 336, 514, 423 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 336, 514, 423?

Answer: HCF of 336, 514, 423 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 336, 514, 423 using Euclid's Algorithm?

Answer: For arbitrary numbers 336, 514, 423 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.