Highest Common Factor of 3975, 6008, 14817 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 3975, 6008, 14817 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3975, 6008, 14817 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 3975, 6008, 14817 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 3975, 6008, 14817 is 1.

HCF(3975, 6008, 14817) = 1

HCF of 3975, 6008, 14817 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 3975, 6008, 14817 is 1.

Highest Common Factor of 3975,6008,14817 using Euclid's algorithm

Highest Common Factor of 3975,6008,14817 is 1

Step 1: Since 6008 > 3975, we apply the division lemma to 6008 and 3975, to get

6008 = 3975 x 1 + 2033

Step 2: Since the reminder 3975 ≠ 0, we apply division lemma to 2033 and 3975, to get

3975 = 2033 x 1 + 1942

Step 3: We consider the new divisor 2033 and the new remainder 1942, and apply the division lemma to get

2033 = 1942 x 1 + 91

We consider the new divisor 1942 and the new remainder 91,and apply the division lemma to get

1942 = 91 x 21 + 31

We consider the new divisor 91 and the new remainder 31,and apply the division lemma to get

91 = 31 x 2 + 29

We consider the new divisor 31 and the new remainder 29,and apply the division lemma to get

31 = 29 x 1 + 2

We consider the new divisor 29 and the new remainder 2,and apply the division lemma to get

29 = 2 x 14 + 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 3975 and 6008 is 1

Notice that 1 = HCF(2,1) = HCF(29,2) = HCF(31,29) = HCF(91,31) = HCF(1942,91) = HCF(2033,1942) = HCF(3975,2033) = HCF(6008,3975) .

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

Step 1: Since 14817 > 1, we apply the division lemma to 14817 and 1, to get

14817 = 1 x 14817 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14817 is 1

Notice that 1 = HCF(14817,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 3975, 6008, 14817 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 3975, 6008, 14817?

Answer: HCF of 3975, 6008, 14817 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3975, 6008, 14817 using Euclid's Algorithm?

Answer: For arbitrary numbers 3975, 6008, 14817 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.