Highest Common Factor of 218, 987, 704 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 218, 987, 704 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 218, 987, 704 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 218, 987, 704 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 218, 987, 704 is 1.

HCF(218, 987, 704) = 1

HCF of 218, 987, 704 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 218, 987, 704 is 1.

Highest Common Factor of 218,987,704 using Euclid's algorithm

Highest Common Factor of 218,987,704 is 1

Step 1: Since 987 > 218, we apply the division lemma to 987 and 218, to get

987 = 218 x 4 + 115

Step 2: Since the reminder 218 ≠ 0, we apply division lemma to 115 and 218, to get

218 = 115 x 1 + 103

Step 3: We consider the new divisor 115 and the new remainder 103, and apply the division lemma to get

115 = 103 x 1 + 12

We consider the new divisor 103 and the new remainder 12,and apply the division lemma to get

103 = 12 x 8 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 218 and 987 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(103,12) = HCF(115,103) = HCF(218,115) = HCF(987,218) .

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

Step 1: Since 704 > 1, we apply the division lemma to 704 and 1, to get

704 = 1 x 704 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 704 is 1

Notice that 1 = HCF(704,1) .

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Frequently Asked Questions on HCF of 218, 987, 704 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 218, 987, 704?

Answer: HCF of 218, 987, 704 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 218, 987, 704 using Euclid's Algorithm?

Answer: For arbitrary numbers 218, 987, 704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.