Highest Common Factor of 786, 498, 255 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 786, 498, 255 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 786, 498, 255 is 3 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 786, 498, 255 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 786, 498, 255 is 3.

HCF(786, 498, 255) = 3

HCF of 786, 498, 255 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 786, 498, 255 is 3.

Highest Common Factor of 786,498,255 using Euclid's algorithm

Highest Common Factor of 786,498,255 is 3

Step 1: Since 786 > 498, we apply the division lemma to 786 and 498, to get

786 = 498 x 1 + 288

Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 288 and 498, to get

498 = 288 x 1 + 210

Step 3: We consider the new divisor 288 and the new remainder 210, and apply the division lemma to get

288 = 210 x 1 + 78

We consider the new divisor 210 and the new remainder 78,and apply the division lemma to get

210 = 78 x 2 + 54

We consider the new divisor 78 and the new remainder 54,and apply the division lemma to get

78 = 54 x 1 + 24

We consider the new divisor 54 and the new remainder 24,and apply the division lemma to get

54 = 24 x 2 + 6

We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get

24 = 6 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 786 and 498 is 6

Notice that 6 = HCF(24,6) = HCF(54,24) = HCF(78,54) = HCF(210,78) = HCF(288,210) = HCF(498,288) = HCF(786,498) .

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

Step 1: Since 255 > 6, we apply the division lemma to 255 and 6, to get

255 = 6 x 42 + 3

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, 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 6 and 255 is 3

Notice that 3 = HCF(6,3) = HCF(255,6) .

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Frequently Asked Questions on HCF of 786, 498, 255 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 786, 498, 255?

Answer: HCF of 786, 498, 255 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 786, 498, 255 using Euclid's Algorithm?

Answer: For arbitrary numbers 786, 498, 255 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.