Highest Common Factor of 610, 842, 421 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 610, 842, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 610, 842, 421 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 610, 842, 421 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 610, 842, 421 is 1.

HCF(610, 842, 421) = 1

HCF of 610, 842, 421 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 610, 842, 421 is 1.

Highest Common Factor of 610,842,421 using Euclid's algorithm

Highest Common Factor of 610,842,421 is 1

Step 1: Since 842 > 610, we apply the division lemma to 842 and 610, to get

842 = 610 x 1 + 232

Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 232 and 610, to get

610 = 232 x 2 + 146

Step 3: We consider the new divisor 232 and the new remainder 146, and apply the division lemma to get

232 = 146 x 1 + 86

We consider the new divisor 146 and the new remainder 86,and apply the division lemma to get

146 = 86 x 1 + 60

We consider the new divisor 86 and the new remainder 60,and apply the division lemma to get

86 = 60 x 1 + 26

We consider the new divisor 60 and the new remainder 26,and apply the division lemma to get

60 = 26 x 2 + 8

We consider the new divisor 26 and the new remainder 8,and apply the division lemma to get

26 = 8 x 3 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 610 and 842 is 2

Notice that 2 = HCF(8,2) = HCF(26,8) = HCF(60,26) = HCF(86,60) = HCF(146,86) = HCF(232,146) = HCF(610,232) = HCF(842,610) .

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

Step 1: Since 421 > 2, we apply the division lemma to 421 and 2, to get

421 = 2 x 210 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 421 is 1

Notice that 1 = HCF(2,1) = HCF(421,2) .

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Frequently Asked Questions on HCF of 610, 842, 421 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 610, 842, 421?

Answer: HCF of 610, 842, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 610, 842, 421 using Euclid's Algorithm?

Answer: For arbitrary numbers 610, 842, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.