Highest Common Factor of 1785, 509 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 1785, 509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1785, 509 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 1785, 509 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 1785, 509 is 1.

HCF(1785, 509) = 1

HCF of 1785, 509 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 1785, 509 is 1.

Highest Common Factor of 1785,509 using Euclid's algorithm

Highest Common Factor of 1785,509 is 1

Step 1: Since 1785 > 509, we apply the division lemma to 1785 and 509, to get

1785 = 509 x 3 + 258

Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 258 and 509, to get

509 = 258 x 1 + 251

Step 3: We consider the new divisor 258 and the new remainder 251, and apply the division lemma to get

258 = 251 x 1 + 7

We consider the new divisor 251 and the new remainder 7,and apply the division lemma to get

251 = 7 x 35 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1785 and 509 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(251,7) = HCF(258,251) = HCF(509,258) = HCF(1785,509) .

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Frequently Asked Questions on HCF of 1785, 509 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 1785, 509?

Answer: HCF of 1785, 509 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1785, 509 using Euclid's Algorithm?

Answer: For arbitrary numbers 1785, 509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.