Highest Common Factor of 506, 7497, 4021 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 506, 7497, 4021 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 506, 7497, 4021 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 506, 7497, 4021 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 506, 7497, 4021 is 1.

HCF(506, 7497, 4021) = 1

HCF of 506, 7497, 4021 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 506, 7497, 4021 is 1.

Highest Common Factor of 506,7497,4021 using Euclid's algorithm

Highest Common Factor of 506,7497,4021 is 1

Step 1: Since 7497 > 506, we apply the division lemma to 7497 and 506, to get

7497 = 506 x 14 + 413

Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 413 and 506, to get

506 = 413 x 1 + 93

Step 3: We consider the new divisor 413 and the new remainder 93, and apply the division lemma to get

413 = 93 x 4 + 41

We consider the new divisor 93 and the new remainder 41,and apply the division lemma to get

93 = 41 x 2 + 11

We consider the new divisor 41 and the new remainder 11,and apply the division lemma to get

41 = 11 x 3 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 506 and 7497 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(41,11) = HCF(93,41) = HCF(413,93) = HCF(506,413) = HCF(7497,506) .

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

Step 1: Since 4021 > 1, we apply the division lemma to 4021 and 1, to get

4021 = 1 x 4021 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 4021 is 1

Notice that 1 = HCF(4021,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 506, 7497, 4021 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 506, 7497, 4021?

Answer: HCF of 506, 7497, 4021 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 506, 7497, 4021 using Euclid's Algorithm?

Answer: For arbitrary numbers 506, 7497, 4021 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.