Highest Common Factor of 2177, 9760 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 2177, 9760 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2177, 9760 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 2177, 9760 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 2177, 9760 is 1.

HCF(2177, 9760) = 1

HCF of 2177, 9760 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 2177, 9760 is 1.

Highest Common Factor of 2177,9760 using Euclid's algorithm

Highest Common Factor of 2177,9760 is 1

Step 1: Since 9760 > 2177, we apply the division lemma to 9760 and 2177, to get

9760 = 2177 x 4 + 1052

Step 2: Since the reminder 2177 ≠ 0, we apply division lemma to 1052 and 2177, to get

2177 = 1052 x 2 + 73

Step 3: We consider the new divisor 1052 and the new remainder 73, and apply the division lemma to get

1052 = 73 x 14 + 30

We consider the new divisor 73 and the new remainder 30,and apply the division lemma to get

73 = 30 x 2 + 13

We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get

30 = 13 x 2 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2177 and 9760 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(73,30) = HCF(1052,73) = HCF(2177,1052) = HCF(9760,2177) .

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Frequently Asked Questions on HCF of 2177, 9760 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 2177, 9760?

Answer: HCF of 2177, 9760 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2177, 9760 using Euclid's Algorithm?

Answer: For arbitrary numbers 2177, 9760 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.