Highest Common Factor of 461, 679, 214 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 461, 679, 214 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 461, 679, 214 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 461, 679, 214 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 461, 679, 214 is 1.

HCF(461, 679, 214) = 1

HCF of 461, 679, 214 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 461, 679, 214 is 1.

Highest Common Factor of 461,679,214 using Euclid's algorithm

Highest Common Factor of 461,679,214 is 1

Step 1: Since 679 > 461, we apply the division lemma to 679 and 461, to get

679 = 461 x 1 + 218

Step 2: Since the reminder 461 ≠ 0, we apply division lemma to 218 and 461, to get

461 = 218 x 2 + 25

Step 3: We consider the new divisor 218 and the new remainder 25, and apply the division lemma to get

218 = 25 x 8 + 18

We consider the new divisor 25 and the new remainder 18,and apply the division lemma to get

25 = 18 x 1 + 7

We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get

18 = 7 x 2 + 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 461 and 679 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(25,18) = HCF(218,25) = HCF(461,218) = HCF(679,461) .

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

Step 1: Since 214 > 1, we apply the division lemma to 214 and 1, to get

214 = 1 x 214 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 214 is 1

Notice that 1 = HCF(214,1) .

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Frequently Asked Questions on HCF of 461, 679, 214 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 461, 679, 214?

Answer: HCF of 461, 679, 214 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 461, 679, 214 using Euclid's Algorithm?

Answer: For arbitrary numbers 461, 679, 214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.