Highest Common Factor of 765, 497 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 765, 497 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 765, 497 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 765, 497 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 765, 497 is 1.

HCF(765, 497) = 1

HCF of 765, 497 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 765, 497 is 1.

Highest Common Factor of 765,497 using Euclid's algorithm

Highest Common Factor of 765,497 is 1

Step 1: Since 765 > 497, we apply the division lemma to 765 and 497, to get

765 = 497 x 1 + 268

Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 268 and 497, to get

497 = 268 x 1 + 229

Step 3: We consider the new divisor 268 and the new remainder 229, and apply the division lemma to get

268 = 229 x 1 + 39

We consider the new divisor 229 and the new remainder 39,and apply the division lemma to get

229 = 39 x 5 + 34

We consider the new divisor 39 and the new remainder 34,and apply the division lemma to get

39 = 34 x 1 + 5

We consider the new divisor 34 and the new remainder 5,and apply the division lemma to get

34 = 5 x 6 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 765 and 497 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(34,5) = HCF(39,34) = HCF(229,39) = HCF(268,229) = HCF(497,268) = HCF(765,497) .

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Frequently Asked Questions on HCF of 765, 497 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 765, 497?

Answer: HCF of 765, 497 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 765, 497 using Euclid's Algorithm?

Answer: For arbitrary numbers 765, 497 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.