Highest Common Factor of 514, 316, 49 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 514, 316, 49 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 514, 316, 49 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 514, 316, 49 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 514, 316, 49 is 1.

HCF(514, 316, 49) = 1

HCF of 514, 316, 49 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 514, 316, 49 is 1.

Highest Common Factor of 514,316,49 using Euclid's algorithm

Highest Common Factor of 514,316,49 is 1

Step 1: Since 514 > 316, we apply the division lemma to 514 and 316, to get

514 = 316 x 1 + 198

Step 2: Since the reminder 316 ≠ 0, we apply division lemma to 198 and 316, to get

316 = 198 x 1 + 118

Step 3: We consider the new divisor 198 and the new remainder 118, and apply the division lemma to get

198 = 118 x 1 + 80

We consider the new divisor 118 and the new remainder 80,and apply the division lemma to get

118 = 80 x 1 + 38

We consider the new divisor 80 and the new remainder 38,and apply the division lemma to get

80 = 38 x 2 + 4

We consider the new divisor 38 and the new remainder 4,and apply the division lemma to get

38 = 4 x 9 + 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 514 and 316 is 2

Notice that 2 = HCF(4,2) = HCF(38,4) = HCF(80,38) = HCF(118,80) = HCF(198,118) = HCF(316,198) = HCF(514,316) .

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

Step 1: Since 49 > 2, we apply the division lemma to 49 and 2, to get

49 = 2 x 24 + 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 49 is 1

Notice that 1 = HCF(2,1) = HCF(49,2) .

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Frequently Asked Questions on HCF of 514, 316, 49 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 514, 316, 49?

Answer: HCF of 514, 316, 49 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 514, 316, 49 using Euclid's Algorithm?

Answer: For arbitrary numbers 514, 316, 49 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.