Highest Common Factor of 712, 375, 493 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, 375, 493 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 712, 375, 493 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 712, 375, 493 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, 375, 493 is 1.

HCF(712, 375, 493) = 1

HCF of 712, 375, 493 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, 375, 493 is 1.

Highest Common Factor of 712,375,493 using Euclid's algorithm

Highest Common Factor of 712,375,493 is 1

Step 1: Since 712 > 375, we apply the division lemma to 712 and 375, to get

712 = 375 x 1 + 337

Step 2: Since the reminder 375 ≠ 0, we apply division lemma to 337 and 375, to get

375 = 337 x 1 + 38

Step 3: We consider the new divisor 337 and the new remainder 38, and apply the division lemma to get

337 = 38 x 8 + 33

We consider the new divisor 38 and the new remainder 33,and apply the division lemma to get

38 = 33 x 1 + 5

We consider the new divisor 33 and the new remainder 5,and apply the division lemma to get

33 = 5 x 6 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 712 and 375 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(33,5) = HCF(38,33) = HCF(337,38) = HCF(375,337) = HCF(712,375) .

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

Step 1: Since 493 > 1, we apply the division lemma to 493 and 1, to get

493 = 1 x 493 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 493 is 1

Notice that 1 = HCF(493,1) .

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Frequently Asked Questions on HCF of 712, 375, 493 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, 375, 493?

Answer: HCF of 712, 375, 493 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 712, 375, 493 using Euclid's Algorithm?

Answer: For arbitrary numbers 712, 375, 493 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.