Highest Common Factor of 505, 810, 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 505, 810, 774 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 505, 810, 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 505, 810, 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 505, 810, 774 is 1.

HCF(505, 810, 774) = 1

HCF of 505, 810, 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 505, 810, 774 is 1.

Highest Common Factor of 505,810,774 using Euclid's algorithm

Highest Common Factor of 505,810,774 is 1

Step 1: Since 810 > 505, we apply the division lemma to 810 and 505, to get

810 = 505 x 1 + 305

Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 305 and 505, to get

505 = 305 x 1 + 200

Step 3: We consider the new divisor 305 and the new remainder 200, and apply the division lemma to get

305 = 200 x 1 + 105

We consider the new divisor 200 and the new remainder 105,and apply the division lemma to get

200 = 105 x 1 + 95

We consider the new divisor 105 and the new remainder 95,and apply the division lemma to get

105 = 95 x 1 + 10

We consider the new divisor 95 and the new remainder 10,and apply the division lemma to get

95 = 10 x 9 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 505 and 810 is 5

Notice that 5 = HCF(10,5) = HCF(95,10) = HCF(105,95) = HCF(200,105) = HCF(305,200) = HCF(505,305) = HCF(810,505) .

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

Step 1: Since 774 > 5, we apply the division lemma to 774 and 5, to get

774 = 5 x 154 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: 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 5 and 774 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(774,5) .

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Frequently Asked Questions on HCF of 505, 810, 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 505, 810, 774?

Answer: HCF of 505, 810, 774 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 505, 810, 774 using Euclid's Algorithm?

Answer: For arbitrary numbers 505, 810, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.