Highest Common Factor of 2193, 1534, 68473 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 2193, 1534, 68473 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2193, 1534, 68473 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 2193, 1534, 68473 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 2193, 1534, 68473 is 1.

HCF(2193, 1534, 68473) = 1

HCF of 2193, 1534, 68473 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 2193, 1534, 68473 is 1.

Highest Common Factor of 2193,1534,68473 using Euclid's algorithm

Highest Common Factor of 2193,1534,68473 is 1

Step 1: Since 2193 > 1534, we apply the division lemma to 2193 and 1534, to get

2193 = 1534 x 1 + 659

Step 2: Since the reminder 1534 ≠ 0, we apply division lemma to 659 and 1534, to get

1534 = 659 x 2 + 216

Step 3: We consider the new divisor 659 and the new remainder 216, and apply the division lemma to get

659 = 216 x 3 + 11

We consider the new divisor 216 and the new remainder 11,and apply the division lemma to get

216 = 11 x 19 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2193 and 1534 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(216,11) = HCF(659,216) = HCF(1534,659) = HCF(2193,1534) .

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

Step 1: Since 68473 > 1, we apply the division lemma to 68473 and 1, to get

68473 = 1 x 68473 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68473 is 1

Notice that 1 = HCF(68473,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 2193, 1534, 68473 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 2193, 1534, 68473?

Answer: HCF of 2193, 1534, 68473 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2193, 1534, 68473 using Euclid's Algorithm?

Answer: For arbitrary numbers 2193, 1534, 68473 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.