Highest Common Factor of 453, 765, 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 453, 765, 457 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 453, 765, 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 453, 765, 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 453, 765, 457 is 1.

HCF(453, 765, 457) = 1

HCF of 453, 765, 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 453, 765, 457 is 1.

Highest Common Factor of 453,765,457 using Euclid's algorithm

Highest Common Factor of 453,765,457 is 1

Step 1: Since 765 > 453, we apply the division lemma to 765 and 453, to get

765 = 453 x 1 + 312

Step 2: Since the reminder 453 ≠ 0, we apply division lemma to 312 and 453, to get

453 = 312 x 1 + 141

Step 3: We consider the new divisor 312 and the new remainder 141, and apply the division lemma to get

312 = 141 x 2 + 30

We consider the new divisor 141 and the new remainder 30,and apply the division lemma to get

141 = 30 x 4 + 21

We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get

30 = 21 x 1 + 9

We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get

21 = 9 x 2 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 453 and 765 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(141,30) = HCF(312,141) = HCF(453,312) = HCF(765,453) .

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

Step 1: Since 457 > 3, we apply the division lemma to 457 and 3, to get

457 = 3 x 152 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 457 is 1

Notice that 1 = HCF(3,1) = HCF(457,3) .

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Frequently Asked Questions on HCF of 453, 765, 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 453, 765, 457?

Answer: HCF of 453, 765, 457 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 453, 765, 457 using Euclid's Algorithm?

Answer: For arbitrary numbers 453, 765, 457 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.