Highest Common Factor of 3708, 7355, 91121 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 3708, 7355, 91121 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3708, 7355, 91121 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 3708, 7355, 91121 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 3708, 7355, 91121 is 1.

HCF(3708, 7355, 91121) = 1

HCF of 3708, 7355, 91121 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 3708, 7355, 91121 is 1.

Highest Common Factor of 3708,7355,91121 using Euclid's algorithm

Highest Common Factor of 3708,7355,91121 is 1

Step 1: Since 7355 > 3708, we apply the division lemma to 7355 and 3708, to get

7355 = 3708 x 1 + 3647

Step 2: Since the reminder 3708 ≠ 0, we apply division lemma to 3647 and 3708, to get

3708 = 3647 x 1 + 61

Step 3: We consider the new divisor 3647 and the new remainder 61, and apply the division lemma to get

3647 = 61 x 59 + 48

We consider the new divisor 61 and the new remainder 48,and apply the division lemma to get

61 = 48 x 1 + 13

We consider the new divisor 48 and the new remainder 13,and apply the division lemma to get

48 = 13 x 3 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 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 3708 and 7355 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(48,13) = HCF(61,48) = HCF(3647,61) = HCF(3708,3647) = HCF(7355,3708) .

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

Step 1: Since 91121 > 1, we apply the division lemma to 91121 and 1, to get

91121 = 1 x 91121 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 91121 is 1

Notice that 1 = HCF(91121,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 3708, 7355, 91121 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 3708, 7355, 91121?

Answer: HCF of 3708, 7355, 91121 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3708, 7355, 91121 using Euclid's Algorithm?

Answer: For arbitrary numbers 3708, 7355, 91121 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.