Highest Common Factor of 506, 779, 774 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 506, 779, 774 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 506, 779, 774 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 506, 779, 774 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 506, 779, 774 is 1.

HCF(506, 779, 774) = 1

HCF of 506, 779, 774 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 506, 779, 774 is 1.

Highest Common Factor of 506,779,774 using Euclid's algorithm

Highest Common Factor of 506,779,774 is 1

Step 1: Since 779 > 506, we apply the division lemma to 779 and 506, to get

779 = 506 x 1 + 273

Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 273 and 506, to get

506 = 273 x 1 + 233

Step 3: We consider the new divisor 273 and the new remainder 233, and apply the division lemma to get

273 = 233 x 1 + 40

We consider the new divisor 233 and the new remainder 40,and apply the division lemma to get

233 = 40 x 5 + 33

We consider the new divisor 40 and the new remainder 33,and apply the division lemma to get

40 = 33 x 1 + 7

We consider the new divisor 33 and the new remainder 7,and apply the division lemma to get

33 = 7 x 4 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

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 506 and 779 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(33,7) = HCF(40,33) = HCF(233,40) = HCF(273,233) = HCF(506,273) = HCF(779,506) .

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

Step 1: Since 774 > 1, we apply the division lemma to 774 and 1, to get

774 = 1 x 774 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 774 is 1

Notice that 1 = HCF(774,1) .

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Frequently Asked Questions on HCF of 506, 779, 774 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 506, 779, 774?

Answer: HCF of 506, 779, 774 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 506, 779, 774 using Euclid's Algorithm?

Answer: For arbitrary numbers 506, 779, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.