Highest Common Factor of 2225, 6501 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 2225, 6501 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2225, 6501 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 2225, 6501 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 2225, 6501 is 1.

HCF(2225, 6501) = 1

HCF of 2225, 6501 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 2225, 6501 is 1.

Highest Common Factor of 2225,6501 using Euclid's algorithm

Highest Common Factor of 2225,6501 is 1

Step 1: Since 6501 > 2225, we apply the division lemma to 6501 and 2225, to get

6501 = 2225 x 2 + 2051

Step 2: Since the reminder 2225 ≠ 0, we apply division lemma to 2051 and 2225, to get

2225 = 2051 x 1 + 174

Step 3: We consider the new divisor 2051 and the new remainder 174, and apply the division lemma to get

2051 = 174 x 11 + 137

We consider the new divisor 174 and the new remainder 137,and apply the division lemma to get

174 = 137 x 1 + 37

We consider the new divisor 137 and the new remainder 37,and apply the division lemma to get

137 = 37 x 3 + 26

We consider the new divisor 37 and the new remainder 26,and apply the division lemma to get

37 = 26 x 1 + 11

We consider the new divisor 26 and the new remainder 11,and apply the division lemma to get

26 = 11 x 2 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2225 and 6501 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(26,11) = HCF(37,26) = HCF(137,37) = HCF(174,137) = HCF(2051,174) = HCF(2225,2051) = HCF(6501,2225) .

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Frequently Asked Questions on HCF of 2225, 6501 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 2225, 6501?

Answer: HCF of 2225, 6501 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2225, 6501 using Euclid's Algorithm?

Answer: For arbitrary numbers 2225, 6501 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.