Highest Common Factor of 415, 660, 363 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 415, 660, 363 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 415, 660, 363 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 415, 660, 363 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 415, 660, 363 is 1.

HCF(415, 660, 363) = 1

HCF of 415, 660, 363 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 415, 660, 363 is 1.

Highest Common Factor of 415,660,363 using Euclid's algorithm

Highest Common Factor of 415,660,363 is 1

Step 1: Since 660 > 415, we apply the division lemma to 660 and 415, to get

660 = 415 x 1 + 245

Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 245 and 415, to get

415 = 245 x 1 + 170

Step 3: We consider the new divisor 245 and the new remainder 170, and apply the division lemma to get

245 = 170 x 1 + 75

We consider the new divisor 170 and the new remainder 75,and apply the division lemma to get

170 = 75 x 2 + 20

We consider the new divisor 75 and the new remainder 20,and apply the division lemma to get

75 = 20 x 3 + 15

We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get

20 = 15 x 1 + 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 415 and 660 is 5

Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(75,20) = HCF(170,75) = HCF(245,170) = HCF(415,245) = HCF(660,415) .

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

Step 1: Since 363 > 5, we apply the division lemma to 363 and 5, to get

363 = 5 x 72 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 5 and 363 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(363,5) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 415, 660, 363 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 415, 660, 363?

Answer: HCF of 415, 660, 363 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 415, 660, 363 using Euclid's Algorithm?

Answer: For arbitrary numbers 415, 660, 363 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.