Highest Common Factor of 642, 378, 209 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 642, 378, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 642, 378, 209 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 642, 378, 209 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 642, 378, 209 is 1.

HCF(642, 378, 209) = 1

HCF of 642, 378, 209 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 642, 378, 209 is 1.

Highest Common Factor of 642,378,209 using Euclid's algorithm

Highest Common Factor of 642,378,209 is 1

Step 1: Since 642 > 378, we apply the division lemma to 642 and 378, to get

642 = 378 x 1 + 264

Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 264 and 378, to get

378 = 264 x 1 + 114

Step 3: We consider the new divisor 264 and the new remainder 114, and apply the division lemma to get

264 = 114 x 2 + 36

We consider the new divisor 114 and the new remainder 36,and apply the division lemma to get

114 = 36 x 3 + 6

We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get

36 = 6 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 642 and 378 is 6

Notice that 6 = HCF(36,6) = HCF(114,36) = HCF(264,114) = HCF(378,264) = HCF(642,378) .

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

Step 1: Since 209 > 6, we apply the division lemma to 209 and 6, to get

209 = 6 x 34 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 209 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(209,6) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 642, 378, 209 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 642, 378, 209?

Answer: HCF of 642, 378, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 642, 378, 209 using Euclid's Algorithm?

Answer: For arbitrary numbers 642, 378, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.