Highest Common Factor of 712, 452, 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 712, 452, 512 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 712, 452, 512 is 4 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 712, 452, 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 712, 452, 512 is 4.

HCF(712, 452, 512) = 4

HCF of 712, 452, 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 712, 452, 512 is 4.

Highest Common Factor of 712,452,512 using Euclid's algorithm

Highest Common Factor of 712,452,512 is 4

Step 1: Since 712 > 452, we apply the division lemma to 712 and 452, to get

712 = 452 x 1 + 260

Step 2: Since the reminder 452 ≠ 0, we apply division lemma to 260 and 452, to get

452 = 260 x 1 + 192

Step 3: We consider the new divisor 260 and the new remainder 192, and apply the division lemma to get

260 = 192 x 1 + 68

We consider the new divisor 192 and the new remainder 68,and apply the division lemma to get

192 = 68 x 2 + 56

We consider the new divisor 68 and the new remainder 56,and apply the division lemma to get

68 = 56 x 1 + 12

We consider the new divisor 56 and the new remainder 12,and apply the division lemma to get

56 = 12 x 4 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 712 and 452 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(56,12) = HCF(68,56) = HCF(192,68) = HCF(260,192) = HCF(452,260) = HCF(712,452) .

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

Step 1: Since 512 > 4, we apply the division lemma to 512 and 4, to get

512 = 4 x 128 + 0

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

Notice that 4 = HCF(512,4) .

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Frequently Asked Questions on HCF of 712, 452, 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 712, 452, 512?

Answer: HCF of 712, 452, 512 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 712, 452, 512 using Euclid's Algorithm?

Answer: For arbitrary numbers 712, 452, 512 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.