Highest Common Factor of 186, 477, 232 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, 477, 232 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 186, 477, 232 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, 477, 232 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, 477, 232 is 1.

HCF(186, 477, 232) = 1

HCF of 186, 477, 232 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, 477, 232 is 1.

Highest Common Factor of 186,477,232 using Euclid's algorithm

Highest Common Factor of 186,477,232 is 1

Step 1: Since 477 > 186, we apply the division lemma to 477 and 186, to get

477 = 186 x 2 + 105

Step 2: Since the reminder 186 ≠ 0, we apply division lemma to 105 and 186, to get

186 = 105 x 1 + 81

Step 3: We consider the new divisor 105 and the new remainder 81, and apply the division lemma to get

105 = 81 x 1 + 24

We consider the new divisor 81 and the new remainder 24,and apply the division lemma to get

81 = 24 x 3 + 9

We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get

24 = 9 x 2 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 186 and 477 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(81,24) = HCF(105,81) = HCF(186,105) = HCF(477,186) .

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

Step 1: Since 232 > 3, we apply the division lemma to 232 and 3, to get

232 = 3 x 77 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 232 is 1

Notice that 1 = HCF(3,1) = HCF(232,3) .

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Frequently Asked Questions on HCF of 186, 477, 232 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, 477, 232?

Answer: HCF of 186, 477, 232 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 186, 477, 232 using Euclid's Algorithm?

Answer: For arbitrary numbers 186, 477, 232 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.