Highest Common Factor of 810, 510, 117 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, 510, 117 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 810, 510, 117 is 3 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, 510, 117 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, 510, 117 is 3.

HCF(810, 510, 117) = 3

HCF of 810, 510, 117 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, 510, 117 is 3.

Highest Common Factor of 810,510,117 using Euclid's algorithm

Highest Common Factor of 810,510,117 is 3

Step 1: Since 810 > 510, we apply the division lemma to 810 and 510, to get

810 = 510 x 1 + 300

Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 300 and 510, to get

510 = 300 x 1 + 210

Step 3: We consider the new divisor 300 and the new remainder 210, and apply the division lemma to get

300 = 210 x 1 + 90

We consider the new divisor 210 and the new remainder 90,and apply the division lemma to get

210 = 90 x 2 + 30

We consider the new divisor 90 and the new remainder 30,and apply the division lemma to get

90 = 30 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 810 and 510 is 30

Notice that 30 = HCF(90,30) = HCF(210,90) = HCF(300,210) = HCF(510,300) = HCF(810,510) .

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

Step 1: Since 117 > 30, we apply the division lemma to 117 and 30, to get

117 = 30 x 3 + 27

Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 27 and 30, to get

30 = 27 x 1 + 3

Step 3: We consider the new divisor 27 and the new remainder 3, and apply the division lemma to get

27 = 3 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 30 and 117 is 3

Notice that 3 = HCF(27,3) = HCF(30,27) = HCF(117,30) .

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Frequently Asked Questions on HCF of 810, 510, 117 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, 510, 117?

Answer: HCF of 810, 510, 117 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 810, 510, 117 using Euclid's Algorithm?

Answer: For arbitrary numbers 810, 510, 117 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.