Highest Common Factor of 523, 454, 459 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 523, 454, 459 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 523, 454, 459 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 523, 454, 459 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 523, 454, 459 is 1.

HCF(523, 454, 459) = 1

HCF of 523, 454, 459 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 523, 454, 459 is 1.

Highest Common Factor of 523,454,459 using Euclid's algorithm

Highest Common Factor of 523,454,459 is 1

Step 1: Since 523 > 454, we apply the division lemma to 523 and 454, to get

523 = 454 x 1 + 69

Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 69 and 454, to get

454 = 69 x 6 + 40

Step 3: We consider the new divisor 69 and the new remainder 40, and apply the division lemma to get

69 = 40 x 1 + 29

We consider the new divisor 40 and the new remainder 29,and apply the division lemma to get

40 = 29 x 1 + 11

We consider the new divisor 29 and the new remainder 11,and apply the division lemma to get

29 = 11 x 2 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 523 and 454 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(29,11) = HCF(40,29) = HCF(69,40) = HCF(454,69) = HCF(523,454) .

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

Step 1: Since 459 > 1, we apply the division lemma to 459 and 1, to get

459 = 1 x 459 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 459 is 1

Notice that 1 = HCF(459,1) .

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Frequently Asked Questions on HCF of 523, 454, 459 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 523, 454, 459?

Answer: HCF of 523, 454, 459 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 523, 454, 459 using Euclid's Algorithm?

Answer: For arbitrary numbers 523, 454, 459 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.