Highest Common Factor of 605, 415, 621 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 605, 415, 621 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 605, 415, 621 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 605, 415, 621 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 605, 415, 621 is 1.

HCF(605, 415, 621) = 1

HCF of 605, 415, 621 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 605, 415, 621 is 1.

Highest Common Factor of 605,415,621 using Euclid's algorithm

Highest Common Factor of 605,415,621 is 1

Step 1: Since 605 > 415, we apply the division lemma to 605 and 415, to get

605 = 415 x 1 + 190

Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 190 and 415, to get

415 = 190 x 2 + 35

Step 3: We consider the new divisor 190 and the new remainder 35, and apply the division lemma to get

190 = 35 x 5 + 15

We consider the new divisor 35 and the new remainder 15,and apply the division lemma to get

35 = 15 x 2 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 605 and 415 is 5

Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(190,35) = HCF(415,190) = HCF(605,415) .

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

Step 1: Since 621 > 5, we apply the division lemma to 621 and 5, to get

621 = 5 x 124 + 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 621 is 1

Notice that 1 = HCF(5,1) = HCF(621,5) .

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Frequently Asked Questions on HCF of 605, 415, 621 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 605, 415, 621?

Answer: HCF of 605, 415, 621 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 605, 415, 621 using Euclid's Algorithm?

Answer: For arbitrary numbers 605, 415, 621 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.