Highest Common Factor of 3729, 6759, 30221 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 3729, 6759, 30221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3729, 6759, 30221 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 3729, 6759, 30221 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 3729, 6759, 30221 is 1.

HCF(3729, 6759, 30221) = 1

HCF of 3729, 6759, 30221 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 3729, 6759, 30221 is 1.

Highest Common Factor of 3729,6759,30221 using Euclid's algorithm

Highest Common Factor of 3729,6759,30221 is 1

Step 1: Since 6759 > 3729, we apply the division lemma to 6759 and 3729, to get

6759 = 3729 x 1 + 3030

Step 2: Since the reminder 3729 ≠ 0, we apply division lemma to 3030 and 3729, to get

3729 = 3030 x 1 + 699

Step 3: We consider the new divisor 3030 and the new remainder 699, and apply the division lemma to get

3030 = 699 x 4 + 234

We consider the new divisor 699 and the new remainder 234,and apply the division lemma to get

699 = 234 x 2 + 231

We consider the new divisor 234 and the new remainder 231,and apply the division lemma to get

234 = 231 x 1 + 3

We consider the new divisor 231 and the new remainder 3,and apply the division lemma to get

231 = 3 x 77 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3729 and 6759 is 3

Notice that 3 = HCF(231,3) = HCF(234,231) = HCF(699,234) = HCF(3030,699) = HCF(3729,3030) = HCF(6759,3729) .

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

Step 1: Since 30221 > 3, we apply the division lemma to 30221 and 3, to get

30221 = 3 x 10073 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 30221 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(30221,3) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 3729, 6759, 30221 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 3729, 6759, 30221?

Answer: HCF of 3729, 6759, 30221 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3729, 6759, 30221 using Euclid's Algorithm?

Answer: For arbitrary numbers 3729, 6759, 30221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.