Highest Common Factor of 680, 255, 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 680, 255, 186 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 680, 255, 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 680, 255, 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 680, 255, 186 is 1.

HCF(680, 255, 186) = 1

HCF of 680, 255, 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 680, 255, 186 is 1.

Highest Common Factor of 680,255,186 using Euclid's algorithm

Highest Common Factor of 680,255,186 is 1

Step 1: Since 680 > 255, we apply the division lemma to 680 and 255, to get

680 = 255 x 2 + 170

Step 2: Since the reminder 255 ≠ 0, we apply division lemma to 170 and 255, to get

255 = 170 x 1 + 85

Step 3: We consider the new divisor 170 and the new remainder 85, and apply the division lemma to get

170 = 85 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 85, the HCF of 680 and 255 is 85

Notice that 85 = HCF(170,85) = HCF(255,170) = HCF(680,255) .

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

Step 1: Since 186 > 85, we apply the division lemma to 186 and 85, to get

186 = 85 x 2 + 16

Step 2: Since the reminder 85 ≠ 0, we apply division lemma to 16 and 85, to get

85 = 16 x 5 + 5

Step 3: We consider the new divisor 16 and the new remainder 5, and apply the division lemma to get

16 = 5 x 3 + 1

We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 85 and 186 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(85,16) = HCF(186,85) .

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Frequently Asked Questions on HCF of 680, 255, 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 680, 255, 186?

Answer: HCF of 680, 255, 186 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 680, 255, 186 using Euclid's Algorithm?

Answer: For arbitrary numbers 680, 255, 186 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.