Highest Common Factor of 77, 666, 186 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 77, 666, 186 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 77, 666, 186 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 77, 666, 186 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 77, 666, 186 is 1.

HCF(77, 666, 186) = 1

HCF of 77, 666, 186 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 77, 666, 186 is 1.

Highest Common Factor of 77,666,186 using Euclid's algorithm

Highest Common Factor of 77,666,186 is 1

Step 1: Since 666 > 77, we apply the division lemma to 666 and 77, to get

666 = 77 x 8 + 50

Step 2: Since the reminder 77 ≠ 0, we apply division lemma to 50 and 77, to get

77 = 50 x 1 + 27

Step 3: We consider the new divisor 50 and the new remainder 27, and apply the division lemma to get

50 = 27 x 1 + 23

We consider the new divisor 27 and the new remainder 23,and apply the division lemma to get

27 = 23 x 1 + 4

We consider the new divisor 23 and the new remainder 4,and apply the division lemma to get

23 = 4 x 5 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 77 and 666 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(23,4) = HCF(27,23) = HCF(50,27) = HCF(77,50) = HCF(666,77) .

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

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

186 = 1 x 186 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 186 is 1

Notice that 1 = HCF(186,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 77, 666, 186 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 77, 666, 186?

Answer: HCF of 77, 666, 186 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 77, 666, 186 using Euclid's Algorithm?

Answer: For arbitrary numbers 77, 666, 186 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.