Highest Common Factor of 668, 806, 360, 866 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 668, 806, 360, 866 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 668, 806, 360, 866 is 2 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 668, 806, 360, 866 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 668, 806, 360, 866 is 2.

HCF(668, 806, 360, 866) = 2

HCF of 668, 806, 360, 866 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 668, 806, 360, 866 is 2.

Highest Common Factor of 668,806,360,866 using Euclid's algorithm

Highest Common Factor of 668,806,360,866 is 2

Step 1: Since 806 > 668, we apply the division lemma to 806 and 668, to get

806 = 668 x 1 + 138

Step 2: Since the reminder 668 ≠ 0, we apply division lemma to 138 and 668, to get

668 = 138 x 4 + 116

Step 3: We consider the new divisor 138 and the new remainder 116, and apply the division lemma to get

138 = 116 x 1 + 22

We consider the new divisor 116 and the new remainder 22,and apply the division lemma to get

116 = 22 x 5 + 6

We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get

22 = 6 x 3 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 668 and 806 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(116,22) = HCF(138,116) = HCF(668,138) = HCF(806,668) .

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

Step 1: Since 360 > 2, we apply the division lemma to 360 and 2, to get

360 = 2 x 180 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 360 is 2

Notice that 2 = HCF(360,2) .

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

Step 1: Since 866 > 2, we apply the division lemma to 866 and 2, to get

866 = 2 x 433 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 866 is 2

Notice that 2 = HCF(866,2) .

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Frequently Asked Questions on HCF of 668, 806, 360, 866 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 668, 806, 360, 866?

Answer: HCF of 668, 806, 360, 866 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 668, 806, 360, 866 using Euclid's Algorithm?

Answer: For arbitrary numbers 668, 806, 360, 866 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.