Highest Common Factor of 274, 871, 147 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 274, 871, 147 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 274, 871, 147 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 274, 871, 147 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 274, 871, 147 is 1.

HCF(274, 871, 147) = 1

HCF of 274, 871, 147 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 274, 871, 147 is 1.

Highest Common Factor of 274,871,147 using Euclid's algorithm

Highest Common Factor of 274,871,147 is 1

Step 1: Since 871 > 274, we apply the division lemma to 871 and 274, to get

871 = 274 x 3 + 49

Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 49 and 274, to get

274 = 49 x 5 + 29

Step 3: We consider the new divisor 49 and the new remainder 29, and apply the division lemma to get

49 = 29 x 1 + 20

We consider the new divisor 29 and the new remainder 20,and apply the division lemma to get

29 = 20 x 1 + 9

We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get

20 = 9 x 2 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 274 and 871 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(29,20) = HCF(49,29) = HCF(274,49) = HCF(871,274) .

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

Step 1: Since 147 > 1, we apply the division lemma to 147 and 1, to get

147 = 1 x 147 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 147 is 1

Notice that 1 = HCF(147,1) .

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Frequently Asked Questions on HCF of 274, 871, 147 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 274, 871, 147?

Answer: HCF of 274, 871, 147 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 274, 871, 147 using Euclid's Algorithm?

Answer: For arbitrary numbers 274, 871, 147 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.