Highest Common Factor of 466, 261, 409, 578 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 466, 261, 409, 578 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 466, 261, 409, 578 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 466, 261, 409, 578 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 466, 261, 409, 578 is 1.

HCF(466, 261, 409, 578) = 1

HCF of 466, 261, 409, 578 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 466, 261, 409, 578 is 1.

Highest Common Factor of 466,261,409,578 using Euclid's algorithm

Highest Common Factor of 466,261,409,578 is 1

Step 1: Since 466 > 261, we apply the division lemma to 466 and 261, to get

466 = 261 x 1 + 205

Step 2: Since the reminder 261 ≠ 0, we apply division lemma to 205 and 261, to get

261 = 205 x 1 + 56

Step 3: We consider the new divisor 205 and the new remainder 56, and apply the division lemma to get

205 = 56 x 3 + 37

We consider the new divisor 56 and the new remainder 37,and apply the division lemma to get

56 = 37 x 1 + 19

We consider the new divisor 37 and the new remainder 19,and apply the division lemma to get

37 = 19 x 1 + 18

We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get

19 = 18 x 1 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 466 and 261 is 1

Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(56,37) = HCF(205,56) = HCF(261,205) = HCF(466,261) .

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

Step 1: Since 409 > 1, we apply the division lemma to 409 and 1, to get

409 = 1 x 409 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 409 is 1

Notice that 1 = HCF(409,1) .

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

Step 1: Since 578 > 1, we apply the division lemma to 578 and 1, to get

578 = 1 x 578 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 578 is 1

Notice that 1 = HCF(578,1) .

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Frequently Asked Questions on HCF of 466, 261, 409, 578 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 466, 261, 409, 578?

Answer: HCF of 466, 261, 409, 578 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 466, 261, 409, 578 using Euclid's Algorithm?

Answer: For arbitrary numbers 466, 261, 409, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.