Highest Common Factor of 341, 896, 872 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 341, 896, 872 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 341, 896, 872 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 341, 896, 872 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 341, 896, 872 is 1.

HCF(341, 896, 872) = 1

HCF of 341, 896, 872 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 341, 896, 872 is 1.

Highest Common Factor of 341,896,872 using Euclid's algorithm

Highest Common Factor of 341,896,872 is 1

Step 1: Since 896 > 341, we apply the division lemma to 896 and 341, to get

896 = 341 x 2 + 214

Step 2: Since the reminder 341 ≠ 0, we apply division lemma to 214 and 341, to get

341 = 214 x 1 + 127

Step 3: We consider the new divisor 214 and the new remainder 127, and apply the division lemma to get

214 = 127 x 1 + 87

We consider the new divisor 127 and the new remainder 87,and apply the division lemma to get

127 = 87 x 1 + 40

We consider the new divisor 87 and the new remainder 40,and apply the division lemma to get

87 = 40 x 2 + 7

We consider the new divisor 40 and the new remainder 7,and apply the division lemma to get

40 = 7 x 5 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 341 and 896 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(40,7) = HCF(87,40) = HCF(127,87) = HCF(214,127) = HCF(341,214) = HCF(896,341) .

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

Step 1: Since 872 > 1, we apply the division lemma to 872 and 1, to get

872 = 1 x 872 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 872 is 1

Notice that 1 = HCF(872,1) .

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Frequently Asked Questions on HCF of 341, 896, 872 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 341, 896, 872?

Answer: HCF of 341, 896, 872 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 341, 896, 872 using Euclid's Algorithm?

Answer: For arbitrary numbers 341, 896, 872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.