Highest Common Factor of 2212, 6507 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 2212, 6507 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2212, 6507 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 2212, 6507 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 2212, 6507 is 1.

HCF(2212, 6507) = 1

HCF of 2212, 6507 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 2212, 6507 is 1.

Highest Common Factor of 2212,6507 using Euclid's algorithm

Highest Common Factor of 2212,6507 is 1

Step 1: Since 6507 > 2212, we apply the division lemma to 6507 and 2212, to get

6507 = 2212 x 2 + 2083

Step 2: Since the reminder 2212 ≠ 0, we apply division lemma to 2083 and 2212, to get

2212 = 2083 x 1 + 129

Step 3: We consider the new divisor 2083 and the new remainder 129, and apply the division lemma to get

2083 = 129 x 16 + 19

We consider the new divisor 129 and the new remainder 19,and apply the division lemma to get

129 = 19 x 6 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 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 2212 and 6507 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(129,19) = HCF(2083,129) = HCF(2212,2083) = HCF(6507,2212) .

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Frequently Asked Questions on HCF of 2212, 6507 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 2212, 6507?

Answer: HCF of 2212, 6507 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2212, 6507 using Euclid's Algorithm?

Answer: For arbitrary numbers 2212, 6507 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.