Highest Common Factor of 419, 690 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, 690 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 419, 690 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, 690 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, 690 is 1.

HCF(419, 690) = 1

HCF of 419, 690 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, 690 is 1.

Highest Common Factor of 419,690 using Euclid's algorithm

Highest Common Factor of 419,690 is 1

Step 1: Since 690 > 419, we apply the division lemma to 690 and 419, to get

690 = 419 x 1 + 271

Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 271 and 419, to get

419 = 271 x 1 + 148

Step 3: We consider the new divisor 271 and the new remainder 148, and apply the division lemma to get

271 = 148 x 1 + 123

We consider the new divisor 148 and the new remainder 123,and apply the division lemma to get

148 = 123 x 1 + 25

We consider the new divisor 123 and the new remainder 25,and apply the division lemma to get

123 = 25 x 4 + 23

We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get

25 = 23 x 1 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 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 690 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(123,25) = HCF(148,123) = HCF(271,148) = HCF(419,271) = HCF(690,419) .

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Frequently Asked Questions on HCF of 419, 690 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, 690?

Answer: HCF of 419, 690 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 419, 690 using Euclid's Algorithm?

Answer: For arbitrary numbers 419, 690 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.