Highest Common Factor of 186, 542, 230 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, 542, 230 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 186, 542, 230 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 186, 542, 230 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, 542, 230 is 2.

HCF(186, 542, 230) = 2

HCF of 186, 542, 230 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, 542, 230 is 2.

Highest Common Factor of 186,542,230 using Euclid's algorithm

Highest Common Factor of 186,542,230 is 2

Step 1: Since 542 > 186, we apply the division lemma to 542 and 186, to get

542 = 186 x 2 + 170

Step 2: Since the reminder 186 ≠ 0, we apply division lemma to 170 and 186, to get

186 = 170 x 1 + 16

Step 3: We consider the new divisor 170 and the new remainder 16, and apply the division lemma to get

170 = 16 x 10 + 10

We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get

16 = 10 x 1 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 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 186 and 542 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(170,16) = HCF(186,170) = HCF(542,186) .

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

Step 1: Since 230 > 2, we apply the division lemma to 230 and 2, to get

230 = 2 x 115 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 230 is 2

Notice that 2 = HCF(230,2) .

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Frequently Asked Questions on HCF of 186, 542, 230 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, 542, 230?

Answer: HCF of 186, 542, 230 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 186, 542, 230 using Euclid's Algorithm?

Answer: For arbitrary numbers 186, 542, 230 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.