Highest Common Factor of 390, 217, 913, 353 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 390, 217, 913, 353 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 390, 217, 913, 353 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 390, 217, 913, 353 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 390, 217, 913, 353 is 1.

HCF(390, 217, 913, 353) = 1

HCF of 390, 217, 913, 353 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 390, 217, 913, 353 is 1.

Highest Common Factor of 390,217,913,353 using Euclid's algorithm

Highest Common Factor of 390,217,913,353 is 1

Step 1: Since 390 > 217, we apply the division lemma to 390 and 217, to get

390 = 217 x 1 + 173

Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 173 and 217, to get

217 = 173 x 1 + 44

Step 3: We consider the new divisor 173 and the new remainder 44, and apply the division lemma to get

173 = 44 x 3 + 41

We consider the new divisor 44 and the new remainder 41,and apply the division lemma to get

44 = 41 x 1 + 3

We consider the new divisor 41 and the new remainder 3,and apply the division lemma to get

41 = 3 x 13 + 2

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 390 and 217 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(41,3) = HCF(44,41) = HCF(173,44) = HCF(217,173) = HCF(390,217) .

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

Step 1: Since 913 > 1, we apply the division lemma to 913 and 1, to get

913 = 1 x 913 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 913 is 1

Notice that 1 = HCF(913,1) .

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

Step 1: Since 353 > 1, we apply the division lemma to 353 and 1, to get

353 = 1 x 353 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 353 is 1

Notice that 1 = HCF(353,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 390, 217, 913, 353 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 390, 217, 913, 353?

Answer: HCF of 390, 217, 913, 353 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 390, 217, 913, 353 using Euclid's Algorithm?

Answer: For arbitrary numbers 390, 217, 913, 353 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.