Highest Common Factor of 905, 523, 654, 600 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 905, 523, 654, 600 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 905, 523, 654, 600 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 905, 523, 654, 600 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 905, 523, 654, 600 is 1.

HCF(905, 523, 654, 600) = 1

HCF of 905, 523, 654, 600 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 905, 523, 654, 600 is 1.

Highest Common Factor of 905,523,654,600 using Euclid's algorithm

Highest Common Factor of 905,523,654,600 is 1

Step 1: Since 905 > 523, we apply the division lemma to 905 and 523, to get

905 = 523 x 1 + 382

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 382 and 523, to get

523 = 382 x 1 + 141

Step 3: We consider the new divisor 382 and the new remainder 141, and apply the division lemma to get

382 = 141 x 2 + 100

We consider the new divisor 141 and the new remainder 100,and apply the division lemma to get

141 = 100 x 1 + 41

We consider the new divisor 100 and the new remainder 41,and apply the division lemma to get

100 = 41 x 2 + 18

We consider the new divisor 41 and the new remainder 18,and apply the division lemma to get

41 = 18 x 2 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 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 905 and 523 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(41,18) = HCF(100,41) = HCF(141,100) = HCF(382,141) = HCF(523,382) = HCF(905,523) .

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

Step 1: Since 654 > 1, we apply the division lemma to 654 and 1, to get

654 = 1 x 654 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 654 is 1

Notice that 1 = HCF(654,1) .

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

Step 1: Since 600 > 1, we apply the division lemma to 600 and 1, to get

600 = 1 x 600 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 600 is 1

Notice that 1 = HCF(600,1) .

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Frequently Asked Questions on HCF of 905, 523, 654, 600 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 905, 523, 654, 600?

Answer: HCF of 905, 523, 654, 600 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 905, 523, 654, 600 using Euclid's Algorithm?

Answer: For arbitrary numbers 905, 523, 654, 600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.