Highest Common Factor of 451, 738, 814 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 451, 738, 814 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 451, 738, 814 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 451, 738, 814 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 451, 738, 814 is 1.

HCF(451, 738, 814) = 1

HCF of 451, 738, 814 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 451, 738, 814 is 1.

Highest Common Factor of 451,738,814 using Euclid's algorithm

Highest Common Factor of 451,738,814 is 1

Step 1: Since 738 > 451, we apply the division lemma to 738 and 451, to get

738 = 451 x 1 + 287

Step 2: Since the reminder 451 ≠ 0, we apply division lemma to 287 and 451, to get

451 = 287 x 1 + 164

Step 3: We consider the new divisor 287 and the new remainder 164, and apply the division lemma to get

287 = 164 x 1 + 123

We consider the new divisor 164 and the new remainder 123,and apply the division lemma to get

164 = 123 x 1 + 41

We consider the new divisor 123 and the new remainder 41,and apply the division lemma to get

123 = 41 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 41, the HCF of 451 and 738 is 41

Notice that 41 = HCF(123,41) = HCF(164,123) = HCF(287,164) = HCF(451,287) = HCF(738,451) .

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

Step 1: Since 814 > 41, we apply the division lemma to 814 and 41, to get

814 = 41 x 19 + 35

Step 2: Since the reminder 41 ≠ 0, we apply division lemma to 35 and 41, to get

41 = 35 x 1 + 6

Step 3: We consider the new divisor 35 and the new remainder 6, and apply the division lemma to get

35 = 6 x 5 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 41 and 814 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(35,6) = HCF(41,35) = HCF(814,41) .

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Frequently Asked Questions on HCF of 451, 738, 814 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 451, 738, 814?

Answer: HCF of 451, 738, 814 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 451, 738, 814 using Euclid's Algorithm?

Answer: For arbitrary numbers 451, 738, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.