Highest Common Factor of 274, 421, 877 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, 421, 877 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 274, 421, 877 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, 421, 877 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, 421, 877 is 1.

HCF(274, 421, 877) = 1

HCF of 274, 421, 877 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, 421, 877 is 1.

Highest Common Factor of 274,421,877 using Euclid's algorithm

Highest Common Factor of 274,421,877 is 1

Step 1: Since 421 > 274, we apply the division lemma to 421 and 274, to get

421 = 274 x 1 + 147

Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 147 and 274, to get

274 = 147 x 1 + 127

Step 3: We consider the new divisor 147 and the new remainder 127, and apply the division lemma to get

147 = 127 x 1 + 20

We consider the new divisor 127 and the new remainder 20,and apply the division lemma to get

127 = 20 x 6 + 7

We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get

20 = 7 x 2 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 274 and 421 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(127,20) = HCF(147,127) = HCF(274,147) = HCF(421,274) .

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

Step 1: Since 877 > 1, we apply the division lemma to 877 and 1, to get

877 = 1 x 877 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 877 is 1

Notice that 1 = HCF(877,1) .

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Frequently Asked Questions on HCF of 274, 421, 877 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, 421, 877?

Answer: HCF of 274, 421, 877 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 274, 421, 877 using Euclid's Algorithm?

Answer: For arbitrary numbers 274, 421, 877 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.