Highest Common Factor of 591, 186, 971 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 591, 186, 971 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 591, 186, 971 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 591, 186, 971 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 591, 186, 971 is 1.

HCF(591, 186, 971) = 1

HCF of 591, 186, 971 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 591, 186, 971 is 1.

Highest Common Factor of 591,186,971 using Euclid's algorithm

Highest Common Factor of 591,186,971 is 1

Step 1: Since 591 > 186, we apply the division lemma to 591 and 186, to get

591 = 186 x 3 + 33

Step 2: Since the reminder 186 ≠ 0, we apply division lemma to 33 and 186, to get

186 = 33 x 5 + 21

Step 3: We consider the new divisor 33 and the new remainder 21, and apply the division lemma to get

33 = 21 x 1 + 12

We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get

21 = 12 x 1 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 591 and 186 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(186,33) = HCF(591,186) .

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

Step 1: Since 971 > 3, we apply the division lemma to 971 and 3, to get

971 = 3 x 323 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 971 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(971,3) .

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Frequently Asked Questions on HCF of 591, 186, 971 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 591, 186, 971?

Answer: HCF of 591, 186, 971 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 591, 186, 971 using Euclid's Algorithm?

Answer: For arbitrary numbers 591, 186, 971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.