Highest Common Factor of 659, 419, 83 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 659, 419, 83 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 659, 419, 83 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 659, 419, 83 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 659, 419, 83 is 1.

HCF(659, 419, 83) = 1

HCF of 659, 419, 83 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 659, 419, 83 is 1.

Highest Common Factor of 659,419,83 using Euclid's algorithm

Highest Common Factor of 659,419,83 is 1

Step 1: Since 659 > 419, we apply the division lemma to 659 and 419, to get

659 = 419 x 1 + 240

Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 240 and 419, to get

419 = 240 x 1 + 179

Step 3: We consider the new divisor 240 and the new remainder 179, and apply the division lemma to get

240 = 179 x 1 + 61

We consider the new divisor 179 and the new remainder 61,and apply the division lemma to get

179 = 61 x 2 + 57

We consider the new divisor 61 and the new remainder 57,and apply the division lemma to get

61 = 57 x 1 + 4

We consider the new divisor 57 and the new remainder 4,and apply the division lemma to get

57 = 4 x 14 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 659 and 419 is 1

Notice that 1 = HCF(4,1) = HCF(57,4) = HCF(61,57) = HCF(179,61) = HCF(240,179) = HCF(419,240) = HCF(659,419) .

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

Step 1: Since 83 > 1, we apply the division lemma to 83 and 1, to get

83 = 1 x 83 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 83 is 1

Notice that 1 = HCF(83,1) .

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Frequently Asked Questions on HCF of 659, 419, 83 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 659, 419, 83?

Answer: HCF of 659, 419, 83 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 659, 419, 83 using Euclid's Algorithm?

Answer: For arbitrary numbers 659, 419, 83 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.