Highest Common Factor of 856, 638, 785 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 856, 638, 785 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 856, 638, 785 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 856, 638, 785 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 856, 638, 785 is 1.

HCF(856, 638, 785) = 1

HCF of 856, 638, 785 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 856, 638, 785 is 1.

Highest Common Factor of 856,638,785 using Euclid's algorithm

Highest Common Factor of 856,638,785 is 1

Step 1: Since 856 > 638, we apply the division lemma to 856 and 638, to get

856 = 638 x 1 + 218

Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 218 and 638, to get

638 = 218 x 2 + 202

Step 3: We consider the new divisor 218 and the new remainder 202, and apply the division lemma to get

218 = 202 x 1 + 16

We consider the new divisor 202 and the new remainder 16,and apply the division lemma to get

202 = 16 x 12 + 10

We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get

16 = 10 x 1 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 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 856 and 638 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(202,16) = HCF(218,202) = HCF(638,218) = HCF(856,638) .

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

Step 1: Since 785 > 2, we apply the division lemma to 785 and 2, to get

785 = 2 x 392 + 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 785 is 1

Notice that 1 = HCF(2,1) = HCF(785,2) .

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Frequently Asked Questions on HCF of 856, 638, 785 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 856, 638, 785?

Answer: HCF of 856, 638, 785 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 856, 638, 785 using Euclid's Algorithm?

Answer: For arbitrary numbers 856, 638, 785 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.