Highest Common Factor of 217, 9500, 3503 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, 9500, 3503 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 217, 9500, 3503 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, 9500, 3503 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, 9500, 3503 is 1.

HCF(217, 9500, 3503) = 1

HCF of 217, 9500, 3503 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, 9500, 3503 is 1.

Highest Common Factor of 217,9500,3503 using Euclid's algorithm

Highest Common Factor of 217,9500,3503 is 1

Step 1: Since 9500 > 217, we apply the division lemma to 9500 and 217, to get

9500 = 217 x 43 + 169

Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 169 and 217, to get

217 = 169 x 1 + 48

Step 3: We consider the new divisor 169 and the new remainder 48, and apply the division lemma to get

169 = 48 x 3 + 25

We consider the new divisor 48 and the new remainder 25,and apply the division lemma to get

48 = 25 x 1 + 23

We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get

25 = 23 x 1 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 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 9500 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(48,25) = HCF(169,48) = HCF(217,169) = HCF(9500,217) .

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

Step 1: Since 3503 > 1, we apply the division lemma to 3503 and 1, to get

3503 = 1 x 3503 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3503 is 1

Notice that 1 = HCF(3503,1) .

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Frequently Asked Questions on HCF of 217, 9500, 3503 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, 9500, 3503?

Answer: HCF of 217, 9500, 3503 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 217, 9500, 3503 using Euclid's Algorithm?

Answer: For arbitrary numbers 217, 9500, 3503 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.