Highest Common Factor of 509, 854, 645 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 509, 854, 645 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 509, 854, 645 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 509, 854, 645 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 509, 854, 645 is 1.

HCF(509, 854, 645) = 1

HCF of 509, 854, 645 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 509, 854, 645 is 1.

Highest Common Factor of 509,854,645 using Euclid's algorithm

Highest Common Factor of 509,854,645 is 1

Step 1: Since 854 > 509, we apply the division lemma to 854 and 509, to get

854 = 509 x 1 + 345

Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 345 and 509, to get

509 = 345 x 1 + 164

Step 3: We consider the new divisor 345 and the new remainder 164, and apply the division lemma to get

345 = 164 x 2 + 17

We consider the new divisor 164 and the new remainder 17,and apply the division lemma to get

164 = 17 x 9 + 11

We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get

17 = 11 x 1 + 6

We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get

11 = 6 x 1 + 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 509 and 854 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(164,17) = HCF(345,164) = HCF(509,345) = HCF(854,509) .

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

Step 1: Since 645 > 1, we apply the division lemma to 645 and 1, to get

645 = 1 x 645 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 645 is 1

Notice that 1 = HCF(645,1) .

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Frequently Asked Questions on HCF of 509, 854, 645 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 509, 854, 645?

Answer: HCF of 509, 854, 645 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 509, 854, 645 using Euclid's Algorithm?

Answer: For arbitrary numbers 509, 854, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.