Highest Common Factor of 412, 655, 403 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 412, 655, 403 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 412, 655, 403 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 412, 655, 403 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 412, 655, 403 is 1.

HCF(412, 655, 403) = 1

HCF of 412, 655, 403 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 412, 655, 403 is 1.

Highest Common Factor of 412,655,403 using Euclid's algorithm

Highest Common Factor of 412,655,403 is 1

Step 1: Since 655 > 412, we apply the division lemma to 655 and 412, to get

655 = 412 x 1 + 243

Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 243 and 412, to get

412 = 243 x 1 + 169

Step 3: We consider the new divisor 243 and the new remainder 169, and apply the division lemma to get

243 = 169 x 1 + 74

We consider the new divisor 169 and the new remainder 74,and apply the division lemma to get

169 = 74 x 2 + 21

We consider the new divisor 74 and the new remainder 21,and apply the division lemma to get

74 = 21 x 3 + 11

We consider the new divisor 21 and the new remainder 11,and apply the division lemma to get

21 = 11 x 1 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 412 and 655 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(74,21) = HCF(169,74) = HCF(243,169) = HCF(412,243) = HCF(655,412) .

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

Step 1: Since 403 > 1, we apply the division lemma to 403 and 1, to get

403 = 1 x 403 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 403 is 1

Notice that 1 = HCF(403,1) .

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Frequently Asked Questions on HCF of 412, 655, 403 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 412, 655, 403?

Answer: HCF of 412, 655, 403 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 412, 655, 403 using Euclid's Algorithm?

Answer: For arbitrary numbers 412, 655, 403 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.