Highest Common Factor of 612, 719, 512 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 612, 719, 512 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 612, 719, 512 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 612, 719, 512 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 612, 719, 512 is 1.

HCF(612, 719, 512) = 1

HCF of 612, 719, 512 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 612, 719, 512 is 1.

Highest Common Factor of 612,719,512 using Euclid's algorithm

Highest Common Factor of 612,719,512 is 1

Step 1: Since 719 > 612, we apply the division lemma to 719 and 612, to get

719 = 612 x 1 + 107

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 107 and 612, to get

612 = 107 x 5 + 77

Step 3: We consider the new divisor 107 and the new remainder 77, and apply the division lemma to get

107 = 77 x 1 + 30

We consider the new divisor 77 and the new remainder 30,and apply the division lemma to get

77 = 30 x 2 + 17

We consider the new divisor 30 and the new remainder 17,and apply the division lemma to get

30 = 17 x 1 + 13

We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get

17 = 13 x 1 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma 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 612 and 719 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(30,17) = HCF(77,30) = HCF(107,77) = HCF(612,107) = HCF(719,612) .

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

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

512 = 1 x 512 + 0

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

Notice that 1 = HCF(512,1) .

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Frequently Asked Questions on HCF of 612, 719, 512 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 612, 719, 512?

Answer: HCF of 612, 719, 512 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 612, 719, 512 using Euclid's Algorithm?

Answer: For arbitrary numbers 612, 719, 512 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.