Highest Common Factor of 665, 363, 690 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 665, 363, 690 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 665, 363, 690 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 665, 363, 690 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 665, 363, 690 is 1.

HCF(665, 363, 690) = 1

HCF of 665, 363, 690 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 665, 363, 690 is 1.

Highest Common Factor of 665,363,690 using Euclid's algorithm

Highest Common Factor of 665,363,690 is 1

Step 1: Since 665 > 363, we apply the division lemma to 665 and 363, to get

665 = 363 x 1 + 302

Step 2: Since the reminder 363 ≠ 0, we apply division lemma to 302 and 363, to get

363 = 302 x 1 + 61

Step 3: We consider the new divisor 302 and the new remainder 61, and apply the division lemma to get

302 = 61 x 4 + 58

We consider the new divisor 61 and the new remainder 58,and apply the division lemma to get

61 = 58 x 1 + 3

We consider the new divisor 58 and the new remainder 3,and apply the division lemma to get

58 = 3 x 19 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 665 and 363 is 1

Notice that 1 = HCF(3,1) = HCF(58,3) = HCF(61,58) = HCF(302,61) = HCF(363,302) = HCF(665,363) .

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

Step 1: Since 690 > 1, we apply the division lemma to 690 and 1, to get

690 = 1 x 690 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 690 is 1

Notice that 1 = HCF(690,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 665, 363, 690 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 665, 363, 690?

Answer: HCF of 665, 363, 690 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 665, 363, 690 using Euclid's Algorithm?

Answer: For arbitrary numbers 665, 363, 690 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.