Highest Common Factor of 2177, 3546 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, 3546 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2177, 3546 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, 3546 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, 3546 is 1.

HCF(2177, 3546) = 1

HCF of 2177, 3546 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, 3546 is 1.

Highest Common Factor of 2177,3546 using Euclid's algorithm

Highest Common Factor of 2177,3546 is 1

Step 1: Since 3546 > 2177, we apply the division lemma to 3546 and 2177, to get

3546 = 2177 x 1 + 1369

Step 2: Since the reminder 2177 ≠ 0, we apply division lemma to 1369 and 2177, to get

2177 = 1369 x 1 + 808

Step 3: We consider the new divisor 1369 and the new remainder 808, and apply the division lemma to get

1369 = 808 x 1 + 561

We consider the new divisor 808 and the new remainder 561,and apply the division lemma to get

808 = 561 x 1 + 247

We consider the new divisor 561 and the new remainder 247,and apply the division lemma to get

561 = 247 x 2 + 67

We consider the new divisor 247 and the new remainder 67,and apply the division lemma to get

247 = 67 x 3 + 46

We consider the new divisor 67 and the new remainder 46,and apply the division lemma to get

67 = 46 x 1 + 21

We consider the new divisor 46 and the new remainder 21,and apply the division lemma to get

46 = 21 x 2 + 4

We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get

21 = 4 x 5 + 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 3546 is 1

Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(46,21) = HCF(67,46) = HCF(247,67) = HCF(561,247) = HCF(808,561) = HCF(1369,808) = HCF(2177,1369) = HCF(3546,2177) .

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Frequently Asked Questions on HCF of 2177, 3546 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, 3546?

Answer: HCF of 2177, 3546 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2177, 3546 using Euclid's Algorithm?

Answer: For arbitrary numbers 2177, 3546 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.