Highest Common Factor of 485, 305, 406 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 485, 305, 406 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 485, 305, 406 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 485, 305, 406 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 485, 305, 406 is 1.

HCF(485, 305, 406) = 1

HCF of 485, 305, 406 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 485, 305, 406 is 1.

Highest Common Factor of 485,305,406 using Euclid's algorithm

Highest Common Factor of 485,305,406 is 1

Step 1: Since 485 > 305, we apply the division lemma to 485 and 305, to get

485 = 305 x 1 + 180

Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 180 and 305, to get

305 = 180 x 1 + 125

Step 3: We consider the new divisor 180 and the new remainder 125, and apply the division lemma to get

180 = 125 x 1 + 55

We consider the new divisor 125 and the new remainder 55,and apply the division lemma to get

125 = 55 x 2 + 15

We consider the new divisor 55 and the new remainder 15,and apply the division lemma to get

55 = 15 x 3 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 485 and 305 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(55,15) = HCF(125,55) = HCF(180,125) = HCF(305,180) = HCF(485,305) .

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

Step 1: Since 406 > 5, we apply the division lemma to 406 and 5, to get

406 = 5 x 81 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 406 is 1

Notice that 1 = HCF(5,1) = HCF(406,5) .

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Frequently Asked Questions on HCF of 485, 305, 406 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 485, 305, 406?

Answer: HCF of 485, 305, 406 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 485, 305, 406 using Euclid's Algorithm?

Answer: For arbitrary numbers 485, 305, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.