Highest Common Factor of 33, 217, 821 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 33, 217, 821 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 33, 217, 821 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 33, 217, 821 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 33, 217, 821 is 1.

HCF(33, 217, 821) = 1

HCF of 33, 217, 821 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 33, 217, 821 is 1.

Highest Common Factor of 33,217,821 using Euclid's algorithm

Highest Common Factor of 33,217,821 is 1

Step 1: Since 217 > 33, we apply the division lemma to 217 and 33, to get

217 = 33 x 6 + 19

Step 2: Since the reminder 33 ≠ 0, we apply division lemma to 19 and 33, to get

33 = 19 x 1 + 14

Step 3: We consider the new divisor 19 and the new remainder 14, and apply the division lemma to get

19 = 14 x 1 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 33 and 217 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(33,19) = HCF(217,33) .

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

Step 1: Since 821 > 1, we apply the division lemma to 821 and 1, to get

821 = 1 x 821 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 821 is 1

Notice that 1 = HCF(821,1) .

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Frequently Asked Questions on HCF of 33, 217, 821 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 33, 217, 821?

Answer: HCF of 33, 217, 821 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 33, 217, 821 using Euclid's Algorithm?

Answer: For arbitrary numbers 33, 217, 821 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.