Highest Common Factor of 9900, 6559 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 9900, 6559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9900, 6559 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 9900, 6559 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 9900, 6559 is 1.

HCF(9900, 6559) = 1

HCF of 9900, 6559 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 9900, 6559 is 1.

Highest Common Factor of 9900,6559 using Euclid's algorithm

Highest Common Factor of 9900,6559 is 1

Step 1: Since 9900 > 6559, we apply the division lemma to 9900 and 6559, to get

9900 = 6559 x 1 + 3341

Step 2: Since the reminder 6559 ≠ 0, we apply division lemma to 3341 and 6559, to get

6559 = 3341 x 1 + 3218

Step 3: We consider the new divisor 3341 and the new remainder 3218, and apply the division lemma to get

3341 = 3218 x 1 + 123

We consider the new divisor 3218 and the new remainder 123,and apply the division lemma to get

3218 = 123 x 26 + 20

We consider the new divisor 123 and the new remainder 20,and apply the division lemma to get

123 = 20 x 6 + 3

We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get

20 = 3 x 6 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9900 and 6559 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(123,20) = HCF(3218,123) = HCF(3341,3218) = HCF(6559,3341) = HCF(9900,6559) .

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Frequently Asked Questions on HCF of 9900, 6559 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 9900, 6559?

Answer: HCF of 9900, 6559 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9900, 6559 using Euclid's Algorithm?

Answer: For arbitrary numbers 9900, 6559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.