Highest Common Factor of 817, 972, 213 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 817, 972, 213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 817, 972, 213 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 817, 972, 213 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 817, 972, 213 is 1.

HCF(817, 972, 213) = 1

HCF of 817, 972, 213 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 817, 972, 213 is 1.

Highest Common Factor of 817,972,213 using Euclid's algorithm

Highest Common Factor of 817,972,213 is 1

Step 1: Since 972 > 817, we apply the division lemma to 972 and 817, to get

972 = 817 x 1 + 155

Step 2: Since the reminder 817 ≠ 0, we apply division lemma to 155 and 817, to get

817 = 155 x 5 + 42

Step 3: We consider the new divisor 155 and the new remainder 42, and apply the division lemma to get

155 = 42 x 3 + 29

We consider the new divisor 42 and the new remainder 29,and apply the division lemma to get

42 = 29 x 1 + 13

We consider the new divisor 29 and the new remainder 13,and apply the division lemma to get

29 = 13 x 2 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 817 and 972 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(29,13) = HCF(42,29) = HCF(155,42) = HCF(817,155) = HCF(972,817) .

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

Step 1: Since 213 > 1, we apply the division lemma to 213 and 1, to get

213 = 1 x 213 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 213 is 1

Notice that 1 = HCF(213,1) .

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Frequently Asked Questions on HCF of 817, 972, 213 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 817, 972, 213?

Answer: HCF of 817, 972, 213 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 817, 972, 213 using Euclid's Algorithm?

Answer: For arbitrary numbers 817, 972, 213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.