Highest Common Factor of 476, 277, 674 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 476, 277, 674 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 476, 277, 674 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 476, 277, 674 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 476, 277, 674 is 1.

HCF(476, 277, 674) = 1

HCF of 476, 277, 674 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 476, 277, 674 is 1.

Highest Common Factor of 476,277,674 using Euclid's algorithm

Highest Common Factor of 476,277,674 is 1

Step 1: Since 476 > 277, we apply the division lemma to 476 and 277, to get

476 = 277 x 1 + 199

Step 2: Since the reminder 277 ≠ 0, we apply division lemma to 199 and 277, to get

277 = 199 x 1 + 78

Step 3: We consider the new divisor 199 and the new remainder 78, and apply the division lemma to get

199 = 78 x 2 + 43

We consider the new divisor 78 and the new remainder 43,and apply the division lemma to get

78 = 43 x 1 + 35

We consider the new divisor 43 and the new remainder 35,and apply the division lemma to get

43 = 35 x 1 + 8

We consider the new divisor 35 and the new remainder 8,and apply the division lemma to get

35 = 8 x 4 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 476 and 277 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(35,8) = HCF(43,35) = HCF(78,43) = HCF(199,78) = HCF(277,199) = HCF(476,277) .

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

Step 1: Since 674 > 1, we apply the division lemma to 674 and 1, to get

674 = 1 x 674 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 674 is 1

Notice that 1 = HCF(674,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 476, 277, 674 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 476, 277, 674?

Answer: HCF of 476, 277, 674 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 476, 277, 674 using Euclid's Algorithm?

Answer: For arbitrary numbers 476, 277, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.