Highest Common Factor of 460, 760, 673 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 460, 760, 673 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 460, 760, 673 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 460, 760, 673 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 460, 760, 673 is 1.

HCF(460, 760, 673) = 1

HCF of 460, 760, 673 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 460, 760, 673 is 1.

Highest Common Factor of 460,760,673 using Euclid's algorithm

Highest Common Factor of 460,760,673 is 1

Step 1: Since 760 > 460, we apply the division lemma to 760 and 460, to get

760 = 460 x 1 + 300

Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 300 and 460, to get

460 = 300 x 1 + 160

Step 3: We consider the new divisor 300 and the new remainder 160, and apply the division lemma to get

300 = 160 x 1 + 140

We consider the new divisor 160 and the new remainder 140,and apply the division lemma to get

160 = 140 x 1 + 20

We consider the new divisor 140 and the new remainder 20,and apply the division lemma to get

140 = 20 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 460 and 760 is 20

Notice that 20 = HCF(140,20) = HCF(160,140) = HCF(300,160) = HCF(460,300) = HCF(760,460) .

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

Step 1: Since 673 > 20, we apply the division lemma to 673 and 20, to get

673 = 20 x 33 + 13

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 13 and 20, to get

20 = 13 x 1 + 7

Step 3: We consider the new divisor 13 and the new remainder 7, and apply the division lemma to get

13 = 7 x 1 + 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 20 and 673 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(673,20) .

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Frequently Asked Questions on HCF of 460, 760, 673 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 460, 760, 673?

Answer: HCF of 460, 760, 673 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 460, 760, 673 using Euclid's Algorithm?

Answer: For arbitrary numbers 460, 760, 673 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.