Highest Common Factor of 900, 545, 853 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 900, 545, 853 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 900, 545, 853 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 900, 545, 853 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 900, 545, 853 is 1.

HCF(900, 545, 853) = 1

HCF of 900, 545, 853 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 900, 545, 853 is 1.

Highest Common Factor of 900,545,853 using Euclid's algorithm

Highest Common Factor of 900,545,853 is 1

Step 1: Since 900 > 545, we apply the division lemma to 900 and 545, to get

900 = 545 x 1 + 355

Step 2: Since the reminder 545 ≠ 0, we apply division lemma to 355 and 545, to get

545 = 355 x 1 + 190

Step 3: We consider the new divisor 355 and the new remainder 190, and apply the division lemma to get

355 = 190 x 1 + 165

We consider the new divisor 190 and the new remainder 165,and apply the division lemma to get

190 = 165 x 1 + 25

We consider the new divisor 165 and the new remainder 25,and apply the division lemma to get

165 = 25 x 6 + 15

We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get

25 = 15 x 1 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 900 and 545 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(165,25) = HCF(190,165) = HCF(355,190) = HCF(545,355) = HCF(900,545) .

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

Step 1: Since 853 > 5, we apply the division lemma to 853 and 5, to get

853 = 5 x 170 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 853 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(853,5) .

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Frequently Asked Questions on HCF of 900, 545, 853 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 900, 545, 853?

Answer: HCF of 900, 545, 853 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 900, 545, 853 using Euclid's Algorithm?

Answer: For arbitrary numbers 900, 545, 853 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.