Highest Common Factor of 679, 420, 337 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 679, 420, 337 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 679, 420, 337 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 679, 420, 337 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 679, 420, 337 is 1.

HCF(679, 420, 337) = 1

HCF of 679, 420, 337 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 679, 420, 337 is 1.

Highest Common Factor of 679,420,337 using Euclid's algorithm

Highest Common Factor of 679,420,337 is 1

Step 1: Since 679 > 420, we apply the division lemma to 679 and 420, to get

679 = 420 x 1 + 259

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 259 and 420, to get

420 = 259 x 1 + 161

Step 3: We consider the new divisor 259 and the new remainder 161, and apply the division lemma to get

259 = 161 x 1 + 98

We consider the new divisor 161 and the new remainder 98,and apply the division lemma to get

161 = 98 x 1 + 63

We consider the new divisor 98 and the new remainder 63,and apply the division lemma to get

98 = 63 x 1 + 35

We consider the new divisor 63 and the new remainder 35,and apply the division lemma to get

63 = 35 x 1 + 28

We consider the new divisor 35 and the new remainder 28,and apply the division lemma to get

35 = 28 x 1 + 7

We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get

28 = 7 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 679 and 420 is 7

Notice that 7 = HCF(28,7) = HCF(35,28) = HCF(63,35) = HCF(98,63) = HCF(161,98) = HCF(259,161) = HCF(420,259) = HCF(679,420) .

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

Step 1: Since 337 > 7, we apply the division lemma to 337 and 7, to get

337 = 7 x 48 + 1

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 337 is 1

Notice that 1 = HCF(7,1) = HCF(337,7) .

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Frequently Asked Questions on HCF of 679, 420, 337 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 679, 420, 337?

Answer: HCF of 679, 420, 337 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 679, 420, 337 using Euclid's Algorithm?

Answer: For arbitrary numbers 679, 420, 337 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.