Highest Common Factor of 3975, 6416 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, 6416 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3975, 6416 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, 6416 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, 6416 is 1.

HCF(3975, 6416) = 1

HCF of 3975, 6416 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, 6416 is 1.

Highest Common Factor of 3975,6416 using Euclid's algorithm

Highest Common Factor of 3975,6416 is 1

Step 1: Since 6416 > 3975, we apply the division lemma to 6416 and 3975, to get

6416 = 3975 x 1 + 2441

Step 2: Since the reminder 3975 ≠ 0, we apply division lemma to 2441 and 3975, to get

3975 = 2441 x 1 + 1534

Step 3: We consider the new divisor 2441 and the new remainder 1534, and apply the division lemma to get

2441 = 1534 x 1 + 907

We consider the new divisor 1534 and the new remainder 907,and apply the division lemma to get

1534 = 907 x 1 + 627

We consider the new divisor 907 and the new remainder 627,and apply the division lemma to get

907 = 627 x 1 + 280

We consider the new divisor 627 and the new remainder 280,and apply the division lemma to get

627 = 280 x 2 + 67

We consider the new divisor 280 and the new remainder 67,and apply the division lemma to get

280 = 67 x 4 + 12

We consider the new divisor 67 and the new remainder 12,and apply the division lemma to get

67 = 12 x 5 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 6416 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(67,12) = HCF(280,67) = HCF(627,280) = HCF(907,627) = HCF(1534,907) = HCF(2441,1534) = HCF(3975,2441) = HCF(6416,3975) .

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, 6416 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, 6416?

Answer: HCF of 3975, 6416 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3975, 6416 using Euclid's Algorithm?

Answer: For arbitrary numbers 3975, 6416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.