Highest Common Factor of 673, 474 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 673, 474 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 673, 474 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 673, 474 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 673, 474 is 1.

HCF(673, 474) = 1

HCF of 673, 474 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 673, 474 is 1.

Highest Common Factor of 673,474 using Euclid's algorithm

Highest Common Factor of 673,474 is 1

Step 1: Since 673 > 474, we apply the division lemma to 673 and 474, to get

673 = 474 x 1 + 199

Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 199 and 474, to get

474 = 199 x 2 + 76

Step 3: We consider the new divisor 199 and the new remainder 76, and apply the division lemma to get

199 = 76 x 2 + 47

We consider the new divisor 76 and the new remainder 47,and apply the division lemma to get

76 = 47 x 1 + 29

We consider the new divisor 47 and the new remainder 29,and apply the division lemma to get

47 = 29 x 1 + 18

We consider the new divisor 29 and the new remainder 18,and apply the division lemma to get

29 = 18 x 1 + 11

We consider the new divisor 18 and the new remainder 11,and apply the division lemma to get

18 = 11 x 1 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 673 and 474 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(29,18) = HCF(47,29) = HCF(76,47) = HCF(199,76) = HCF(474,199) = HCF(673,474) .

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Frequently Asked Questions on HCF of 673, 474 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 673, 474?

Answer: HCF of 673, 474 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 673, 474 using Euclid's Algorithm?

Answer: For arbitrary numbers 673, 474 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.