Highest Common Factor of 217, 614, 172, 53 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, 614, 172, 53 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 217, 614, 172, 53 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, 614, 172, 53 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, 614, 172, 53 is 1.

HCF(217, 614, 172, 53) = 1

HCF of 217, 614, 172, 53 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, 614, 172, 53 is 1.

Highest Common Factor of 217,614,172,53 using Euclid's algorithm

Highest Common Factor of 217,614,172,53 is 1

Step 1: Since 614 > 217, we apply the division lemma to 614 and 217, to get

614 = 217 x 2 + 180

Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 180 and 217, to get

217 = 180 x 1 + 37

Step 3: We consider the new divisor 180 and the new remainder 37, and apply the division lemma to get

180 = 37 x 4 + 32

We consider the new divisor 37 and the new remainder 32,and apply the division lemma to get

37 = 32 x 1 + 5

We consider the new divisor 32 and the new remainder 5,and apply the division lemma to get

32 = 5 x 6 + 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 217 and 614 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) = HCF(37,32) = HCF(180,37) = HCF(217,180) = HCF(614,217) .

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

Step 1: Since 172 > 1, we apply the division lemma to 172 and 1, to get

172 = 1 x 172 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 172 is 1

Notice that 1 = HCF(172,1) .

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

Step 1: Since 53 > 1, we apply the division lemma to 53 and 1, to get

53 = 1 x 53 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 53 is 1

Notice that 1 = HCF(53,1) .

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Frequently Asked Questions on HCF of 217, 614, 172, 53 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, 614, 172, 53?

Answer: HCF of 217, 614, 172, 53 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 217, 614, 172, 53 using Euclid's Algorithm?

Answer: For arbitrary numbers 217, 614, 172, 53 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.