Highest Common Factor of 419, 688, 610 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, 688, 610 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 419, 688, 610 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, 688, 610 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, 688, 610 is 1.

HCF(419, 688, 610) = 1

HCF of 419, 688, 610 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, 688, 610 is 1.

Highest Common Factor of 419,688,610 using Euclid's algorithm

Highest Common Factor of 419,688,610 is 1

Step 1: Since 688 > 419, we apply the division lemma to 688 and 419, to get

688 = 419 x 1 + 269

Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 269 and 419, to get

419 = 269 x 1 + 150

Step 3: We consider the new divisor 269 and the new remainder 150, and apply the division lemma to get

269 = 150 x 1 + 119

We consider the new divisor 150 and the new remainder 119,and apply the division lemma to get

150 = 119 x 1 + 31

We consider the new divisor 119 and the new remainder 31,and apply the division lemma to get

119 = 31 x 3 + 26

We consider the new divisor 31 and the new remainder 26,and apply the division lemma to get

31 = 26 x 1 + 5

We consider the new divisor 26 and the new remainder 5,and apply the division lemma to get

26 = 5 x 5 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 419 and 688 is 1

Notice that 1 = HCF(5,1) = HCF(26,5) = HCF(31,26) = HCF(119,31) = HCF(150,119) = HCF(269,150) = HCF(419,269) = HCF(688,419) .

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

Step 1: Since 610 > 1, we apply the division lemma to 610 and 1, to get

610 = 1 x 610 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 610 is 1

Notice that 1 = HCF(610,1) .

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Frequently Asked Questions on HCF of 419, 688, 610 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, 688, 610?

Answer: HCF of 419, 688, 610 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 419, 688, 610 using Euclid's Algorithm?

Answer: For arbitrary numbers 419, 688, 610 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.