Highest Common Factor of 186, 865, 390 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 186, 865, 390 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 186, 865, 390 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 186, 865, 390 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 186, 865, 390 is 1.

HCF(186, 865, 390) = 1

HCF of 186, 865, 390 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 186, 865, 390 is 1.

Highest Common Factor of 186,865,390 using Euclid's algorithm

Highest Common Factor of 186,865,390 is 1

Step 1: Since 865 > 186, we apply the division lemma to 865 and 186, to get

865 = 186 x 4 + 121

Step 2: Since the reminder 186 ≠ 0, we apply division lemma to 121 and 186, to get

186 = 121 x 1 + 65

Step 3: We consider the new divisor 121 and the new remainder 65, and apply the division lemma to get

121 = 65 x 1 + 56

We consider the new divisor 65 and the new remainder 56,and apply the division lemma to get

65 = 56 x 1 + 9

We consider the new divisor 56 and the new remainder 9,and apply the division lemma to get

56 = 9 x 6 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 1

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 186 and 865 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(56,9) = HCF(65,56) = HCF(121,65) = HCF(186,121) = HCF(865,186) .

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

Step 1: Since 390 > 1, we apply the division lemma to 390 and 1, to get

390 = 1 x 390 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 390 is 1

Notice that 1 = HCF(390,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 186, 865, 390 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 186, 865, 390?

Answer: HCF of 186, 865, 390 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 186, 865, 390 using Euclid's Algorithm?

Answer: For arbitrary numbers 186, 865, 390 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.