Highest Common Factor of 812, 512, 905 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 812, 512, 905 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 812, 512, 905 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 812, 512, 905 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 812, 512, 905 is 1.

HCF(812, 512, 905) = 1

HCF of 812, 512, 905 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 812, 512, 905 is 1.

Highest Common Factor of 812,512,905 using Euclid's algorithm

Highest Common Factor of 812,512,905 is 1

Step 1: Since 812 > 512, we apply the division lemma to 812 and 512, to get

812 = 512 x 1 + 300

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 300 and 512, to get

512 = 300 x 1 + 212

Step 3: We consider the new divisor 300 and the new remainder 212, and apply the division lemma to get

300 = 212 x 1 + 88

We consider the new divisor 212 and the new remainder 88,and apply the division lemma to get

212 = 88 x 2 + 36

We consider the new divisor 88 and the new remainder 36,and apply the division lemma to get

88 = 36 x 2 + 16

We consider the new divisor 36 and the new remainder 16,and apply the division lemma to get

36 = 16 x 2 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 812 and 512 is 4

Notice that 4 = HCF(16,4) = HCF(36,16) = HCF(88,36) = HCF(212,88) = HCF(300,212) = HCF(512,300) = HCF(812,512) .

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

Step 1: Since 905 > 4, we apply the division lemma to 905 and 4, to get

905 = 4 x 226 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 905 is 1

Notice that 1 = HCF(4,1) = HCF(905,4) .

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Frequently Asked Questions on HCF of 812, 512, 905 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 812, 512, 905?

Answer: HCF of 812, 512, 905 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 812, 512, 905 using Euclid's Algorithm?

Answer: For arbitrary numbers 812, 512, 905 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.