Highest Common Factor of 3760, 7735, 32669 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 3760, 7735, 32669 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3760, 7735, 32669 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 3760, 7735, 32669 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 3760, 7735, 32669 is 1.

HCF(3760, 7735, 32669) = 1

HCF of 3760, 7735, 32669 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 3760, 7735, 32669 is 1.

Highest Common Factor of 3760,7735,32669 using Euclid's algorithm

Highest Common Factor of 3760,7735,32669 is 1

Step 1: Since 7735 > 3760, we apply the division lemma to 7735 and 3760, to get

7735 = 3760 x 2 + 215

Step 2: Since the reminder 3760 ≠ 0, we apply division lemma to 215 and 3760, to get

3760 = 215 x 17 + 105

Step 3: We consider the new divisor 215 and the new remainder 105, and apply the division lemma to get

215 = 105 x 2 + 5

We consider the new divisor 105 and the new remainder 5, and apply the division lemma to get

105 = 5 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 3760 and 7735 is 5

Notice that 5 = HCF(105,5) = HCF(215,105) = HCF(3760,215) = HCF(7735,3760) .

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

Step 1: Since 32669 > 5, we apply the division lemma to 32669 and 5, to get

32669 = 5 x 6533 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: 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 5 and 32669 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(32669,5) .

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Frequently Asked Questions on HCF of 3760, 7735, 32669 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 3760, 7735, 32669?

Answer: HCF of 3760, 7735, 32669 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3760, 7735, 32669 using Euclid's Algorithm?

Answer: For arbitrary numbers 3760, 7735, 32669 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.