Highest Common Factor of 666, 377, 773 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 666, 377, 773 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 666, 377, 773 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 666, 377, 773 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 666, 377, 773 is 1.

HCF(666, 377, 773) = 1

HCF of 666, 377, 773 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 666, 377, 773 is 1.

Highest Common Factor of 666,377,773 using Euclid's algorithm

Highest Common Factor of 666,377,773 is 1

Step 1: Since 666 > 377, we apply the division lemma to 666 and 377, to get

666 = 377 x 1 + 289

Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 289 and 377, to get

377 = 289 x 1 + 88

Step 3: We consider the new divisor 289 and the new remainder 88, and apply the division lemma to get

289 = 88 x 3 + 25

We consider the new divisor 88 and the new remainder 25,and apply the division lemma to get

88 = 25 x 3 + 13

We consider the new divisor 25 and the new remainder 13,and apply the division lemma to get

25 = 13 x 1 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 666 and 377 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(25,13) = HCF(88,25) = HCF(289,88) = HCF(377,289) = HCF(666,377) .

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

Step 1: Since 773 > 1, we apply the division lemma to 773 and 1, to get

773 = 1 x 773 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 773 is 1

Notice that 1 = HCF(773,1) .

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Frequently Asked Questions on HCF of 666, 377, 773 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 666, 377, 773?

Answer: HCF of 666, 377, 773 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 666, 377, 773 using Euclid's Algorithm?

Answer: For arbitrary numbers 666, 377, 773 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.