Highest Common Factor of 6173, 3208 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 6173, 3208 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6173, 3208 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 6173, 3208 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 6173, 3208 is 1.

HCF(6173, 3208) = 1

HCF of 6173, 3208 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 6173, 3208 is 1.

Highest Common Factor of 6173,3208 using Euclid's algorithm

Highest Common Factor of 6173,3208 is 1

Step 1: Since 6173 > 3208, we apply the division lemma to 6173 and 3208, to get

6173 = 3208 x 1 + 2965

Step 2: Since the reminder 3208 ≠ 0, we apply division lemma to 2965 and 3208, to get

3208 = 2965 x 1 + 243

Step 3: We consider the new divisor 2965 and the new remainder 243, and apply the division lemma to get

2965 = 243 x 12 + 49

We consider the new divisor 243 and the new remainder 49,and apply the division lemma to get

243 = 49 x 4 + 47

We consider the new divisor 49 and the new remainder 47,and apply the division lemma to get

49 = 47 x 1 + 2

We consider the new divisor 47 and the new remainder 2,and apply the division lemma to get

47 = 2 x 23 + 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 6173 and 3208 is 1

Notice that 1 = HCF(2,1) = HCF(47,2) = HCF(49,47) = HCF(243,49) = HCF(2965,243) = HCF(3208,2965) = HCF(6173,3208) .

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Frequently Asked Questions on HCF of 6173, 3208 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 6173, 3208?

Answer: HCF of 6173, 3208 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6173, 3208 using Euclid's Algorithm?

Answer: For arbitrary numbers 6173, 3208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.