Highest Common Factor of 515, 298, 888 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 515, 298, 888 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 515, 298, 888 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 515, 298, 888 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 515, 298, 888 is 1.

HCF(515, 298, 888) = 1

HCF of 515, 298, 888 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 515, 298, 888 is 1.

Highest Common Factor of 515,298,888 using Euclid's algorithm

Highest Common Factor of 515,298,888 is 1

Step 1: Since 515 > 298, we apply the division lemma to 515 and 298, to get

515 = 298 x 1 + 217

Step 2: Since the reminder 298 ≠ 0, we apply division lemma to 217 and 298, to get

298 = 217 x 1 + 81

Step 3: We consider the new divisor 217 and the new remainder 81, and apply the division lemma to get

217 = 81 x 2 + 55

We consider the new divisor 81 and the new remainder 55,and apply the division lemma to get

81 = 55 x 1 + 26

We consider the new divisor 55 and the new remainder 26,and apply the division lemma to get

55 = 26 x 2 + 3

We consider the new divisor 26 and the new remainder 3,and apply the division lemma to get

26 = 3 x 8 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 515 and 298 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(26,3) = HCF(55,26) = HCF(81,55) = HCF(217,81) = HCF(298,217) = HCF(515,298) .

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

Step 1: Since 888 > 1, we apply the division lemma to 888 and 1, to get

888 = 1 x 888 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 888 is 1

Notice that 1 = HCF(888,1) .

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Frequently Asked Questions on HCF of 515, 298, 888 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 515, 298, 888?

Answer: HCF of 515, 298, 888 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 515, 298, 888 using Euclid's Algorithm?

Answer: For arbitrary numbers 515, 298, 888 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.