Highest Common Factor of 874, 311, 23 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 874, 311, 23 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 874, 311, 23 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 874, 311, 23 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 874, 311, 23 is 1.

HCF(874, 311, 23) = 1

HCF of 874, 311, 23 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 874, 311, 23 is 1.

Highest Common Factor of 874,311,23 using Euclid's algorithm

Highest Common Factor of 874,311,23 is 1

Step 1: Since 874 > 311, we apply the division lemma to 874 and 311, to get

874 = 311 x 2 + 252

Step 2: Since the reminder 311 ≠ 0, we apply division lemma to 252 and 311, to get

311 = 252 x 1 + 59

Step 3: We consider the new divisor 252 and the new remainder 59, and apply the division lemma to get

252 = 59 x 4 + 16

We consider the new divisor 59 and the new remainder 16,and apply the division lemma to get

59 = 16 x 3 + 11

We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 874 and 311 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(59,16) = HCF(252,59) = HCF(311,252) = HCF(874,311) .

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

Step 1: Since 23 > 1, we apply the division lemma to 23 and 1, to get

23 = 1 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 23 is 1

Notice that 1 = HCF(23,1) .

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Frequently Asked Questions on HCF of 874, 311, 23 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 874, 311, 23?

Answer: HCF of 874, 311, 23 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 874, 311, 23 using Euclid's Algorithm?

Answer: For arbitrary numbers 874, 311, 23 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.