Highest Common Factor of 815, 512, 232 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 815, 512, 232 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 815, 512, 232 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 815, 512, 232 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 815, 512, 232 is 1.

HCF(815, 512, 232) = 1

HCF of 815, 512, 232 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 815, 512, 232 is 1.

Highest Common Factor of 815,512,232 using Euclid's algorithm

Highest Common Factor of 815,512,232 is 1

Step 1: Since 815 > 512, we apply the division lemma to 815 and 512, to get

815 = 512 x 1 + 303

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 303 and 512, to get

512 = 303 x 1 + 209

Step 3: We consider the new divisor 303 and the new remainder 209, and apply the division lemma to get

303 = 209 x 1 + 94

We consider the new divisor 209 and the new remainder 94,and apply the division lemma to get

209 = 94 x 2 + 21

We consider the new divisor 94 and the new remainder 21,and apply the division lemma to get

94 = 21 x 4 + 10

We consider the new divisor 21 and the new remainder 10,and apply the division lemma to get

21 = 10 x 2 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 815 and 512 is 1

Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(94,21) = HCF(209,94) = HCF(303,209) = HCF(512,303) = HCF(815,512) .

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

Step 1: Since 232 > 1, we apply the division lemma to 232 and 1, to get

232 = 1 x 232 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 232 is 1

Notice that 1 = HCF(232,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 815, 512, 232 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 815, 512, 232?

Answer: HCF of 815, 512, 232 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 815, 512, 232 using Euclid's Algorithm?

Answer: For arbitrary numbers 815, 512, 232 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.