Highest Common Factor of 498, 765, 776 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 498, 765, 776 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 498, 765, 776 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 498, 765, 776 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 498, 765, 776 is 1.

HCF(498, 765, 776) = 1

HCF of 498, 765, 776 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 498, 765, 776 is 1.

Highest Common Factor of 498,765,776 using Euclid's algorithm

Highest Common Factor of 498,765,776 is 1

Step 1: Since 765 > 498, we apply the division lemma to 765 and 498, to get

765 = 498 x 1 + 267

Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 267 and 498, to get

498 = 267 x 1 + 231

Step 3: We consider the new divisor 267 and the new remainder 231, and apply the division lemma to get

267 = 231 x 1 + 36

We consider the new divisor 231 and the new remainder 36,and apply the division lemma to get

231 = 36 x 6 + 15

We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get

36 = 15 x 2 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 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 498 and 765 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(231,36) = HCF(267,231) = HCF(498,267) = HCF(765,498) .

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

Step 1: Since 776 > 3, we apply the division lemma to 776 and 3, to get

776 = 3 x 258 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 776 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(776,3) .

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Frequently Asked Questions on HCF of 498, 765, 776 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 498, 765, 776?

Answer: HCF of 498, 765, 776 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 498, 765, 776 using Euclid's Algorithm?

Answer: For arbitrary numbers 498, 765, 776 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.