Highest Common Factor of 674, 473, 103 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 674, 473, 103 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 674, 473, 103 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 674, 473, 103 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 674, 473, 103 is 1.

HCF(674, 473, 103) = 1

HCF of 674, 473, 103 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 674, 473, 103 is 1.

Highest Common Factor of 674,473,103 using Euclid's algorithm

Highest Common Factor of 674,473,103 is 1

Step 1: Since 674 > 473, we apply the division lemma to 674 and 473, to get

674 = 473 x 1 + 201

Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 201 and 473, to get

473 = 201 x 2 + 71

Step 3: We consider the new divisor 201 and the new remainder 71, and apply the division lemma to get

201 = 71 x 2 + 59

We consider the new divisor 71 and the new remainder 59,and apply the division lemma to get

71 = 59 x 1 + 12

We consider the new divisor 59 and the new remainder 12,and apply the division lemma to get

59 = 12 x 4 + 11

We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get

12 = 11 x 1 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 674 and 473 is 1

Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(59,12) = HCF(71,59) = HCF(201,71) = HCF(473,201) = HCF(674,473) .

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

Step 1: Since 103 > 1, we apply the division lemma to 103 and 1, to get

103 = 1 x 103 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 103 is 1

Notice that 1 = HCF(103,1) .

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Frequently Asked Questions on HCF of 674, 473, 103 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 674, 473, 103?

Answer: HCF of 674, 473, 103 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 674, 473, 103 using Euclid's Algorithm?

Answer: For arbitrary numbers 674, 473, 103 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.