Highest Common Factor of 774, 490, 405 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 774, 490, 405 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 774, 490, 405 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 774, 490, 405 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 774, 490, 405 is 1.

HCF(774, 490, 405) = 1

HCF of 774, 490, 405 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 774, 490, 405 is 1.

Highest Common Factor of 774,490,405 using Euclid's algorithm

Highest Common Factor of 774,490,405 is 1

Step 1: Since 774 > 490, we apply the division lemma to 774 and 490, to get

774 = 490 x 1 + 284

Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 284 and 490, to get

490 = 284 x 1 + 206

Step 3: We consider the new divisor 284 and the new remainder 206, and apply the division lemma to get

284 = 206 x 1 + 78

We consider the new divisor 206 and the new remainder 78,and apply the division lemma to get

206 = 78 x 2 + 50

We consider the new divisor 78 and the new remainder 50,and apply the division lemma to get

78 = 50 x 1 + 28

We consider the new divisor 50 and the new remainder 28,and apply the division lemma to get

50 = 28 x 1 + 22

We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get

28 = 22 x 1 + 6

We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get

22 = 6 x 3 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 774 and 490 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(50,28) = HCF(78,50) = HCF(206,78) = HCF(284,206) = HCF(490,284) = HCF(774,490) .

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

Step 1: Since 405 > 2, we apply the division lemma to 405 and 2, to get

405 = 2 x 202 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 405 is 1

Notice that 1 = HCF(2,1) = HCF(405,2) .

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Frequently Asked Questions on HCF of 774, 490, 405 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 774, 490, 405?

Answer: HCF of 774, 490, 405 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 774, 490, 405 using Euclid's Algorithm?

Answer: For arbitrary numbers 774, 490, 405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.