Highest Common Factor of 815, 506, 988 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 815, 506, 988 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 815, 506, 988 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 815, 506, 988 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 815, 506, 988 is 1.

HCF(815, 506, 988) = 1

HCF of 815, 506, 988 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 815, 506, 988 is 1.

Highest Common Factor of 815,506,988 using Euclid's algorithm

Highest Common Factor of 815,506,988 is 1

Step 1: Since 815 > 506, we apply the division lemma to 815 and 506, to get

815 = 506 x 1 + 309

Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 309 and 506, to get

506 = 309 x 1 + 197

Step 3: We consider the new divisor 309 and the new remainder 197, and apply the division lemma to get

309 = 197 x 1 + 112

We consider the new divisor 197 and the new remainder 112,and apply the division lemma to get

197 = 112 x 1 + 85

We consider the new divisor 112 and the new remainder 85,and apply the division lemma to get

112 = 85 x 1 + 27

We consider the new divisor 85 and the new remainder 27,and apply the division lemma to get

85 = 27 x 3 + 4

We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get

27 = 4 x 6 + 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 815 and 506 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(85,27) = HCF(112,85) = HCF(197,112) = HCF(309,197) = HCF(506,309) = HCF(815,506) .

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

Step 1: Since 988 > 1, we apply the division lemma to 988 and 1, to get

988 = 1 x 988 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 988 is 1

Notice that 1 = HCF(988,1) .

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Frequently Asked Questions on HCF of 815, 506, 988 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 815, 506, 988?

Answer: HCF of 815, 506, 988 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 815, 506, 988 using Euclid's Algorithm?

Answer: For arbitrary numbers 815, 506, 988 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.