Highest Common Factor of 810, 674, 147 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 810, 674, 147 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 810, 674, 147 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 810, 674, 147 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 810, 674, 147 is 1.

HCF(810, 674, 147) = 1

HCF of 810, 674, 147 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 810, 674, 147 is 1.

Highest Common Factor of 810,674,147 using Euclid's algorithm

Highest Common Factor of 810,674,147 is 1

Step 1: Since 810 > 674, we apply the division lemma to 810 and 674, to get

810 = 674 x 1 + 136

Step 2: Since the reminder 674 ≠ 0, we apply division lemma to 136 and 674, to get

674 = 136 x 4 + 130

Step 3: We consider the new divisor 136 and the new remainder 130, and apply the division lemma to get

136 = 130 x 1 + 6

We consider the new divisor 130 and the new remainder 6,and apply the division lemma to get

130 = 6 x 21 + 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 810 and 674 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(130,6) = HCF(136,130) = HCF(674,136) = HCF(810,674) .

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

Step 1: Since 147 > 2, we apply the division lemma to 147 and 2, to get

147 = 2 x 73 + 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 147 is 1

Notice that 1 = HCF(2,1) = HCF(147,2) .

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Frequently Asked Questions on HCF of 810, 674, 147 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 810, 674, 147?

Answer: HCF of 810, 674, 147 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 810, 674, 147 using Euclid's Algorithm?

Answer: For arbitrary numbers 810, 674, 147 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.