Highest Common Factor of 230, 345, 641 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 230, 345, 641 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 230, 345, 641 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 230, 345, 641 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 230, 345, 641 is 1.

HCF(230, 345, 641) = 1

HCF of 230, 345, 641 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 230, 345, 641 is 1.

Highest Common Factor of 230,345,641 using Euclid's algorithm

Highest Common Factor of 230,345,641 is 1

Step 1: Since 345 > 230, we apply the division lemma to 345 and 230, to get

345 = 230 x 1 + 115

Step 2: Since the reminder 230 ≠ 0, we apply division lemma to 115 and 230, to get

230 = 115 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 115, the HCF of 230 and 345 is 115

Notice that 115 = HCF(230,115) = HCF(345,230) .

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

Step 1: Since 641 > 115, we apply the division lemma to 641 and 115, to get

641 = 115 x 5 + 66

Step 2: Since the reminder 115 ≠ 0, we apply division lemma to 66 and 115, to get

115 = 66 x 1 + 49

Step 3: We consider the new divisor 66 and the new remainder 49, and apply the division lemma to get

66 = 49 x 1 + 17

We consider the new divisor 49 and the new remainder 17,and apply the division lemma to get

49 = 17 x 2 + 15

We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get

17 = 15 x 1 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 115 and 641 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(49,17) = HCF(66,49) = HCF(115,66) = HCF(641,115) .

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Frequently Asked Questions on HCF of 230, 345, 641 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 230, 345, 641?

Answer: HCF of 230, 345, 641 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 230, 345, 641 using Euclid's Algorithm?

Answer: For arbitrary numbers 230, 345, 641 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.