Highest Common Factor of 419, 679, 148 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 419, 679, 148 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 419, 679, 148 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 419, 679, 148 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 419, 679, 148 is 1.

HCF(419, 679, 148) = 1

HCF of 419, 679, 148 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 419, 679, 148 is 1.

Highest Common Factor of 419,679,148 using Euclid's algorithm

Highest Common Factor of 419,679,148 is 1

Step 1: Since 679 > 419, we apply the division lemma to 679 and 419, to get

679 = 419 x 1 + 260

Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 260 and 419, to get

419 = 260 x 1 + 159

Step 3: We consider the new divisor 260 and the new remainder 159, and apply the division lemma to get

260 = 159 x 1 + 101

We consider the new divisor 159 and the new remainder 101,and apply the division lemma to get

159 = 101 x 1 + 58

We consider the new divisor 101 and the new remainder 58,and apply the division lemma to get

101 = 58 x 1 + 43

We consider the new divisor 58 and the new remainder 43,and apply the division lemma to get

58 = 43 x 1 + 15

We consider the new divisor 43 and the new remainder 15,and apply the division lemma to get

43 = 15 x 2 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 419 and 679 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(43,15) = HCF(58,43) = HCF(101,58) = HCF(159,101) = HCF(260,159) = HCF(419,260) = HCF(679,419) .

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

Step 1: Since 148 > 1, we apply the division lemma to 148 and 1, to get

148 = 1 x 148 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 148 is 1

Notice that 1 = HCF(148,1) .

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Frequently Asked Questions on HCF of 419, 679, 148 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 419, 679, 148?

Answer: HCF of 419, 679, 148 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 419, 679, 148 using Euclid's Algorithm?

Answer: For arbitrary numbers 419, 679, 148 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.