Highest Common Factor of 523, 705, 217 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 523, 705, 217 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 523, 705, 217 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 523, 705, 217 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 523, 705, 217 is 1.

HCF(523, 705, 217) = 1

HCF of 523, 705, 217 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 523, 705, 217 is 1.

Highest Common Factor of 523,705,217 using Euclid's algorithm

Highest Common Factor of 523,705,217 is 1

Step 1: Since 705 > 523, we apply the division lemma to 705 and 523, to get

705 = 523 x 1 + 182

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 182 and 523, to get

523 = 182 x 2 + 159

Step 3: We consider the new divisor 182 and the new remainder 159, and apply the division lemma to get

182 = 159 x 1 + 23

We consider the new divisor 159 and the new remainder 23,and apply the division lemma to get

159 = 23 x 6 + 21

We consider the new divisor 23 and the new remainder 21,and apply the division lemma to get

23 = 21 x 1 + 2

We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get

21 = 2 x 10 + 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 523 and 705 is 1

Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(159,23) = HCF(182,159) = HCF(523,182) = HCF(705,523) .

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

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

217 = 1 x 217 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 217 is 1

Notice that 1 = HCF(217,1) .

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Frequently Asked Questions on HCF of 523, 705, 217 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 523, 705, 217?

Answer: HCF of 523, 705, 217 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 523, 705, 217 using Euclid's Algorithm?

Answer: For arbitrary numbers 523, 705, 217 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.