Highest Common Factor of 785, 2154 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 785, 2154 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 785, 2154 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 785, 2154 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 785, 2154 is 1.

HCF(785, 2154) = 1

HCF of 785, 2154 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 785, 2154 is 1.

Highest Common Factor of 785,2154 using Euclid's algorithm

Highest Common Factor of 785,2154 is 1

Step 1: Since 2154 > 785, we apply the division lemma to 2154 and 785, to get

2154 = 785 x 2 + 584

Step 2: Since the reminder 785 ≠ 0, we apply division lemma to 584 and 785, to get

785 = 584 x 1 + 201

Step 3: We consider the new divisor 584 and the new remainder 201, and apply the division lemma to get

584 = 201 x 2 + 182

We consider the new divisor 201 and the new remainder 182,and apply the division lemma to get

201 = 182 x 1 + 19

We consider the new divisor 182 and the new remainder 19,and apply the division lemma to get

182 = 19 x 9 + 11

We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 785 and 2154 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(182,19) = HCF(201,182) = HCF(584,201) = HCF(785,584) = HCF(2154,785) .

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Frequently Asked Questions on HCF of 785, 2154 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 785, 2154?

Answer: HCF of 785, 2154 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 785, 2154 using Euclid's Algorithm?

Answer: For arbitrary numbers 785, 2154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.