Highest Common Factor of 419, 663, 67 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, 663, 67 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 419, 663, 67 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, 663, 67 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, 663, 67 is 1.

HCF(419, 663, 67) = 1

HCF of 419, 663, 67 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, 663, 67 is 1.

Highest Common Factor of 419,663,67 using Euclid's algorithm

Highest Common Factor of 419,663,67 is 1

Step 1: Since 663 > 419, we apply the division lemma to 663 and 419, to get

663 = 419 x 1 + 244

Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 244 and 419, to get

419 = 244 x 1 + 175

Step 3: We consider the new divisor 244 and the new remainder 175, and apply the division lemma to get

244 = 175 x 1 + 69

We consider the new divisor 175 and the new remainder 69,and apply the division lemma to get

175 = 69 x 2 + 37

We consider the new divisor 69 and the new remainder 37,and apply the division lemma to get

69 = 37 x 1 + 32

We consider the new divisor 37 and the new remainder 32,and apply the division lemma to get

37 = 32 x 1 + 5

We consider the new divisor 32 and the new remainder 5,and apply the division lemma to get

32 = 5 x 6 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 663 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) = HCF(37,32) = HCF(69,37) = HCF(175,69) = HCF(244,175) = HCF(419,244) = HCF(663,419) .

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

Step 1: Since 67 > 1, we apply the division lemma to 67 and 1, to get

67 = 1 x 67 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 67 is 1

Notice that 1 = HCF(67,1) .

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Frequently Asked Questions on HCF of 419, 663, 67 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, 663, 67?

Answer: HCF of 419, 663, 67 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 419, 663, 67 using Euclid's Algorithm?

Answer: For arbitrary numbers 419, 663, 67 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.