Highest Common Factor of 478, 186, 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 478, 186, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 478, 186, 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 478, 186, 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 478, 186, 421 is 1.

HCF(478, 186, 421) = 1

HCF of 478, 186, 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 478, 186, 421 is 1.

Highest Common Factor of 478,186,421 using Euclid's algorithm

Highest Common Factor of 478,186,421 is 1

Step 1: Since 478 > 186, we apply the division lemma to 478 and 186, to get

478 = 186 x 2 + 106

Step 2: Since the reminder 186 ≠ 0, we apply division lemma to 106 and 186, to get

186 = 106 x 1 + 80

Step 3: We consider the new divisor 106 and the new remainder 80, and apply the division lemma to get

106 = 80 x 1 + 26

We consider the new divisor 80 and the new remainder 26,and apply the division lemma to get

80 = 26 x 3 + 2

We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get

26 = 2 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 478 and 186 is 2

Notice that 2 = HCF(26,2) = HCF(80,26) = HCF(106,80) = HCF(186,106) = HCF(478,186) .

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 478, 186, 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 478, 186, 421?

Answer: HCF of 478, 186, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 478, 186, 421 using Euclid's Algorithm?

Answer: For arbitrary numbers 478, 186, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.