Highest Common Factor of 867, 658, 591 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 867, 658, 591 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 867, 658, 591 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 867, 658, 591 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 867, 658, 591 is 1.

HCF(867, 658, 591) = 1

HCF of 867, 658, 591 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 867, 658, 591 is 1.

Highest Common Factor of 867,658,591 using Euclid's algorithm

Highest Common Factor of 867,658,591 is 1

Step 1: Since 867 > 658, we apply the division lemma to 867 and 658, to get

867 = 658 x 1 + 209

Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 209 and 658, to get

658 = 209 x 3 + 31

Step 3: We consider the new divisor 209 and the new remainder 31, and apply the division lemma to get

209 = 31 x 6 + 23

We consider the new divisor 31 and the new remainder 23,and apply the division lemma to get

31 = 23 x 1 + 8

We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get

23 = 8 x 2 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 867 and 658 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(31,23) = HCF(209,31) = HCF(658,209) = HCF(867,658) .

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

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

591 = 1 x 591 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 591 is 1

Notice that 1 = HCF(591,1) .

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Frequently Asked Questions on HCF of 867, 658, 591 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 867, 658, 591?

Answer: HCF of 867, 658, 591 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 867, 658, 591 using Euclid's Algorithm?

Answer: For arbitrary numbers 867, 658, 591 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.