Highest Common Factor of 66, 231, 917 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 66, 231, 917 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 66, 231, 917 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 66, 231, 917 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 66, 231, 917 is 1.

HCF(66, 231, 917) = 1

HCF of 66, 231, 917 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 66, 231, 917 is 1.

Highest Common Factor of 66,231,917 using Euclid's algorithm

Highest Common Factor of 66,231,917 is 1

Step 1: Since 231 > 66, we apply the division lemma to 231 and 66, to get

231 = 66 x 3 + 33

Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 33 and 66, to get

66 = 33 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 33, the HCF of 66 and 231 is 33

Notice that 33 = HCF(66,33) = HCF(231,66) .

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

Step 1: Since 917 > 33, we apply the division lemma to 917 and 33, to get

917 = 33 x 27 + 26

Step 2: Since the reminder 33 ≠ 0, we apply division lemma to 26 and 33, to get

33 = 26 x 1 + 7

Step 3: We consider the new divisor 26 and the new remainder 7, and apply the division lemma to get

26 = 7 x 3 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 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 33 and 917 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(26,7) = HCF(33,26) = HCF(917,33) .

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Frequently Asked Questions on HCF of 66, 231, 917 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 66, 231, 917?

Answer: HCF of 66, 231, 917 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 66, 231, 917 using Euclid's Algorithm?

Answer: For arbitrary numbers 66, 231, 917 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.