Highest Common Factor of 643, 782, 457 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 643, 782, 457 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 643, 782, 457 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 643, 782, 457 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 643, 782, 457 is 1.

HCF(643, 782, 457) = 1

HCF of 643, 782, 457 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 643, 782, 457 is 1.

Highest Common Factor of 643,782,457 using Euclid's algorithm

Highest Common Factor of 643,782,457 is 1

Step 1: Since 782 > 643, we apply the division lemma to 782 and 643, to get

782 = 643 x 1 + 139

Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 139 and 643, to get

643 = 139 x 4 + 87

Step 3: We consider the new divisor 139 and the new remainder 87, and apply the division lemma to get

139 = 87 x 1 + 52

We consider the new divisor 87 and the new remainder 52,and apply the division lemma to get

87 = 52 x 1 + 35

We consider the new divisor 52 and the new remainder 35,and apply the division lemma to get

52 = 35 x 1 + 17

We consider the new divisor 35 and the new remainder 17,and apply the division lemma to get

35 = 17 x 2 + 1

We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get

17 = 1 x 17 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 643 and 782 is 1

Notice that 1 = HCF(17,1) = HCF(35,17) = HCF(52,35) = HCF(87,52) = HCF(139,87) = HCF(643,139) = HCF(782,643) .

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

Step 1: Since 457 > 1, we apply the division lemma to 457 and 1, to get

457 = 1 x 457 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 457 is 1

Notice that 1 = HCF(457,1) .

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Frequently Asked Questions on HCF of 643, 782, 457 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 643, 782, 457?

Answer: HCF of 643, 782, 457 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 643, 782, 457 using Euclid's Algorithm?

Answer: For arbitrary numbers 643, 782, 457 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.