Highest Common Factor of 421, 258 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 421, 258 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 421, 258 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 421, 258 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 421, 258 is 1.

HCF(421, 258) = 1

HCF of 421, 258 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 421, 258 is 1.

Highest Common Factor of 421,258 using Euclid's algorithm

Highest Common Factor of 421,258 is 1

Step 1: Since 421 > 258, we apply the division lemma to 421 and 258, to get

421 = 258 x 1 + 163

Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 163 and 258, to get

258 = 163 x 1 + 95

Step 3: We consider the new divisor 163 and the new remainder 95, and apply the division lemma to get

163 = 95 x 1 + 68

We consider the new divisor 95 and the new remainder 68,and apply the division lemma to get

95 = 68 x 1 + 27

We consider the new divisor 68 and the new remainder 27,and apply the division lemma to get

68 = 27 x 2 + 14

We consider the new divisor 27 and the new remainder 14,and apply the division lemma to get

27 = 14 x 1 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 421 and 258 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(68,27) = HCF(95,68) = HCF(163,95) = HCF(258,163) = HCF(421,258) .

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Frequently Asked Questions on HCF of 421, 258 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 421, 258?

Answer: HCF of 421, 258 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 421, 258 using Euclid's Algorithm?

Answer: For arbitrary numbers 421, 258 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.