Highest Common Factor of 9665, 2227, 65208 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 9665, 2227, 65208 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9665, 2227, 65208 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 9665, 2227, 65208 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 9665, 2227, 65208 is 1.

HCF(9665, 2227, 65208) = 1

HCF of 9665, 2227, 65208 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 9665, 2227, 65208 is 1.

Highest Common Factor of 9665,2227,65208 using Euclid's algorithm

Highest Common Factor of 9665,2227,65208 is 1

Step 1: Since 9665 > 2227, we apply the division lemma to 9665 and 2227, to get

9665 = 2227 x 4 + 757

Step 2: Since the reminder 2227 ≠ 0, we apply division lemma to 757 and 2227, to get

2227 = 757 x 2 + 713

Step 3: We consider the new divisor 757 and the new remainder 713, and apply the division lemma to get

757 = 713 x 1 + 44

We consider the new divisor 713 and the new remainder 44,and apply the division lemma to get

713 = 44 x 16 + 9

We consider the new divisor 44 and the new remainder 9,and apply the division lemma to get

44 = 9 x 4 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9665 and 2227 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(44,9) = HCF(713,44) = HCF(757,713) = HCF(2227,757) = HCF(9665,2227) .

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

Step 1: Since 65208 > 1, we apply the division lemma to 65208 and 1, to get

65208 = 1 x 65208 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 65208 is 1

Notice that 1 = HCF(65208,1) .

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Frequently Asked Questions on HCF of 9665, 2227, 65208 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 9665, 2227, 65208?

Answer: HCF of 9665, 2227, 65208 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9665, 2227, 65208 using Euclid's Algorithm?

Answer: For arbitrary numbers 9665, 2227, 65208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.