Highest Common Factor of 643, 245, 65 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 643, 245, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 643, 245, 65 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 643, 245, 65 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 643, 245, 65 is 1.

HCF(643, 245, 65) = 1

HCF of 643, 245, 65 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 643, 245, 65 is 1.

Highest Common Factor of 643,245,65 using Euclid's algorithm

Highest Common Factor of 643,245,65 is 1

Step 1: Since 643 > 245, we apply the division lemma to 643 and 245, to get

643 = 245 x 2 + 153

Step 2: Since the reminder 245 ≠ 0, we apply division lemma to 153 and 245, to get

245 = 153 x 1 + 92

Step 3: We consider the new divisor 153 and the new remainder 92, and apply the division lemma to get

153 = 92 x 1 + 61

We consider the new divisor 92 and the new remainder 61,and apply the division lemma to get

92 = 61 x 1 + 31

We consider the new divisor 61 and the new remainder 31,and apply the division lemma to get

61 = 31 x 1 + 30

We consider the new divisor 31 and the new remainder 30,and apply the division lemma to get

31 = 30 x 1 + 1

We consider the new divisor 30 and the new remainder 1,and apply the division lemma 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 643 and 245 is 1

Notice that 1 = HCF(30,1) = HCF(31,30) = HCF(61,31) = HCF(92,61) = HCF(153,92) = HCF(245,153) = HCF(643,245) .

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

Step 1: Since 65 > 1, we apply the division lemma to 65 and 1, to get

65 = 1 x 65 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 65 is 1

Notice that 1 = HCF(65,1) .

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Frequently Asked Questions on HCF of 643, 245, 65 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 643, 245, 65?

Answer: HCF of 643, 245, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 643, 245, 65 using Euclid's Algorithm?

Answer: For arbitrary numbers 643, 245, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.