Highest Common Factor of 262, 3623, 6780 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 262, 3623, 6780 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 262, 3623, 6780 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 262, 3623, 6780 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 262, 3623, 6780 is 1.

HCF(262, 3623, 6780) = 1

HCF of 262, 3623, 6780 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 262, 3623, 6780 is 1.

Highest Common Factor of 262,3623,6780 using Euclid's algorithm

Highest Common Factor of 262,3623,6780 is 1

Step 1: Since 3623 > 262, we apply the division lemma to 3623 and 262, to get

3623 = 262 x 13 + 217

Step 2: Since the reminder 262 ≠ 0, we apply division lemma to 217 and 262, to get

262 = 217 x 1 + 45

Step 3: We consider the new divisor 217 and the new remainder 45, and apply the division lemma to get

217 = 45 x 4 + 37

We consider the new divisor 45 and the new remainder 37,and apply the division lemma to get

45 = 37 x 1 + 8

We consider the new divisor 37 and the new remainder 8,and apply the division lemma to get

37 = 8 x 4 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 262 and 3623 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(37,8) = HCF(45,37) = HCF(217,45) = HCF(262,217) = HCF(3623,262) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 6780 > 1, we apply the division lemma to 6780 and 1, to get

6780 = 1 x 6780 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6780 is 1

Notice that 1 = HCF(6780,1) .

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Frequently Asked Questions on HCF of 262, 3623, 6780 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 262, 3623, 6780?

Answer: HCF of 262, 3623, 6780 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 262, 3623, 6780 using Euclid's Algorithm?

Answer: For arbitrary numbers 262, 3623, 6780 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.