Highest Common Factor of 873, 339, 256 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 873, 339, 256 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 873, 339, 256 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 873, 339, 256 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 873, 339, 256 is 1.

HCF(873, 339, 256) = 1

HCF of 873, 339, 256 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 873, 339, 256 is 1.

Highest Common Factor of 873,339,256 using Euclid's algorithm

Highest Common Factor of 873,339,256 is 1

Step 1: Since 873 > 339, we apply the division lemma to 873 and 339, to get

873 = 339 x 2 + 195

Step 2: Since the reminder 339 ≠ 0, we apply division lemma to 195 and 339, to get

339 = 195 x 1 + 144

Step 3: We consider the new divisor 195 and the new remainder 144, and apply the division lemma to get

195 = 144 x 1 + 51

We consider the new divisor 144 and the new remainder 51,and apply the division lemma to get

144 = 51 x 2 + 42

We consider the new divisor 51 and the new remainder 42,and apply the division lemma to get

51 = 42 x 1 + 9

We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get

42 = 9 x 4 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 873 and 339 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(51,42) = HCF(144,51) = HCF(195,144) = HCF(339,195) = HCF(873,339) .

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

Step 1: Since 256 > 3, we apply the division lemma to 256 and 3, to get

256 = 3 x 85 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 256 is 1

Notice that 1 = HCF(3,1) = HCF(256,3) .

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Frequently Asked Questions on HCF of 873, 339, 256 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 873, 339, 256?

Answer: HCF of 873, 339, 256 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 873, 339, 256 using Euclid's Algorithm?

Answer: For arbitrary numbers 873, 339, 256 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.