Highest Common Factor of 514, 690, 296 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, 690, 296 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 514, 690, 296 is 2 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, 690, 296 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, 690, 296 is 2.

HCF(514, 690, 296) = 2

HCF of 514, 690, 296 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 514, 690, 296 is 2.

Highest Common Factor of 514,690,296 using Euclid's algorithm

Highest Common Factor of 514,690,296 is 2

Step 1: Since 690 > 514, we apply the division lemma to 690 and 514, to get

690 = 514 x 1 + 176

Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 176 and 514, to get

514 = 176 x 2 + 162

Step 3: We consider the new divisor 176 and the new remainder 162, and apply the division lemma to get

176 = 162 x 1 + 14

We consider the new divisor 162 and the new remainder 14,and apply the division lemma to get

162 = 14 x 11 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 514 and 690 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(162,14) = HCF(176,162) = HCF(514,176) = HCF(690,514) .

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

Step 1: Since 296 > 2, we apply the division lemma to 296 and 2, to get

296 = 2 x 148 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 296 is 2

Notice that 2 = HCF(296,2) .

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Frequently Asked Questions on HCF of 514, 690, 296 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, 690, 296?

Answer: HCF of 514, 690, 296 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 514, 690, 296 using Euclid's Algorithm?

Answer: For arbitrary numbers 514, 690, 296 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.