Highest Common Factor of 217, 7984, 5845 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 217, 7984, 5845 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 217, 7984, 5845 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 217, 7984, 5845 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 217, 7984, 5845 is 1.

HCF(217, 7984, 5845) = 1

HCF of 217, 7984, 5845 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 217, 7984, 5845 is 1.

Highest Common Factor of 217,7984,5845 using Euclid's algorithm

Highest Common Factor of 217,7984,5845 is 1

Step 1: Since 7984 > 217, we apply the division lemma to 7984 and 217, to get

7984 = 217 x 36 + 172

Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 172 and 217, to get

217 = 172 x 1 + 45

Step 3: We consider the new divisor 172 and the new remainder 45, and apply the division lemma to get

172 = 45 x 3 + 37

We consider the new divisor 45 and the new remainder 37,and apply the division lemma to get

45 = 37 x 1 + 8

We consider the new divisor 37 and the new remainder 8,and apply the division lemma to get

37 = 8 x 4 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 217 and 7984 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(37,8) = HCF(45,37) = HCF(172,45) = HCF(217,172) = HCF(7984,217) .

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

Step 1: Since 5845 > 1, we apply the division lemma to 5845 and 1, to get

5845 = 1 x 5845 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5845 is 1

Notice that 1 = HCF(5845,1) .

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Frequently Asked Questions on HCF of 217, 7984, 5845 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 217, 7984, 5845?

Answer: HCF of 217, 7984, 5845 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 217, 7984, 5845 using Euclid's Algorithm?

Answer: For arbitrary numbers 217, 7984, 5845 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.