Highest Common Factor of 413, 681, 778 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 413, 681, 778 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 413, 681, 778 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 413, 681, 778 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 413, 681, 778 is 1.

HCF(413, 681, 778) = 1

HCF of 413, 681, 778 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 413, 681, 778 is 1.

Highest Common Factor of 413,681,778 using Euclid's algorithm

Highest Common Factor of 413,681,778 is 1

Step 1: Since 681 > 413, we apply the division lemma to 681 and 413, to get

681 = 413 x 1 + 268

Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 268 and 413, to get

413 = 268 x 1 + 145

Step 3: We consider the new divisor 268 and the new remainder 145, and apply the division lemma to get

268 = 145 x 1 + 123

We consider the new divisor 145 and the new remainder 123,and apply the division lemma to get

145 = 123 x 1 + 22

We consider the new divisor 123 and the new remainder 22,and apply the division lemma to get

123 = 22 x 5 + 13

We consider the new divisor 22 and the new remainder 13,and apply the division lemma to get

22 = 13 x 1 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 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 413 and 681 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(123,22) = HCF(145,123) = HCF(268,145) = HCF(413,268) = HCF(681,413) .

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

Step 1: Since 778 > 1, we apply the division lemma to 778 and 1, to get

778 = 1 x 778 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 778 is 1

Notice that 1 = HCF(778,1) .

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Frequently Asked Questions on HCF of 413, 681, 778 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 413, 681, 778?

Answer: HCF of 413, 681, 778 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 413, 681, 778 using Euclid's Algorithm?

Answer: For arbitrary numbers 413, 681, 778 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.