Highest Common Factor of 363, 692, 30 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 363, 692, 30 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 363, 692, 30 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 363, 692, 30 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 363, 692, 30 is 1.

HCF(363, 692, 30) = 1

HCF of 363, 692, 30 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 363, 692, 30 is 1.

Highest Common Factor of 363,692,30 using Euclid's algorithm

Highest Common Factor of 363,692,30 is 1

Step 1: Since 692 > 363, we apply the division lemma to 692 and 363, to get

692 = 363 x 1 + 329

Step 2: Since the reminder 363 ≠ 0, we apply division lemma to 329 and 363, to get

363 = 329 x 1 + 34

Step 3: We consider the new divisor 329 and the new remainder 34, and apply the division lemma to get

329 = 34 x 9 + 23

We consider the new divisor 34 and the new remainder 23,and apply the division lemma to get

34 = 23 x 1 + 11

We consider the new divisor 23 and the new remainder 11,and apply the division lemma to get

23 = 11 x 2 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 363 and 692 is 1

Notice that 1 = HCF(11,1) = HCF(23,11) = HCF(34,23) = HCF(329,34) = HCF(363,329) = HCF(692,363) .

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

Step 1: Since 30 > 1, we apply the division lemma to 30 and 1, to get

30 = 1 x 30 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 30 is 1

Notice that 1 = HCF(30,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 363, 692, 30 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 363, 692, 30?

Answer: HCF of 363, 692, 30 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 363, 692, 30 using Euclid's Algorithm?

Answer: For arbitrary numbers 363, 692, 30 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.