Highest Common Factor of 909, 525, 254 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 909, 525, 254 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 909, 525, 254 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 909, 525, 254 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 909, 525, 254 is 1.

HCF(909, 525, 254) = 1

HCF of 909, 525, 254 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 909, 525, 254 is 1.

Highest Common Factor of 909,525,254 using Euclid's algorithm

Highest Common Factor of 909,525,254 is 1

Step 1: Since 909 > 525, we apply the division lemma to 909 and 525, to get

909 = 525 x 1 + 384

Step 2: Since the reminder 525 ≠ 0, we apply division lemma to 384 and 525, to get

525 = 384 x 1 + 141

Step 3: We consider the new divisor 384 and the new remainder 141, and apply the division lemma to get

384 = 141 x 2 + 102

We consider the new divisor 141 and the new remainder 102,and apply the division lemma to get

141 = 102 x 1 + 39

We consider the new divisor 102 and the new remainder 39,and apply the division lemma to get

102 = 39 x 2 + 24

We consider the new divisor 39 and the new remainder 24,and apply the division lemma to get

39 = 24 x 1 + 15

We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get

24 = 15 x 1 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 909 and 525 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(39,24) = HCF(102,39) = HCF(141,102) = HCF(384,141) = HCF(525,384) = HCF(909,525) .

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

Step 1: Since 254 > 3, we apply the division lemma to 254 and 3, to get

254 = 3 x 84 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 254 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(254,3) .

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Frequently Asked Questions on HCF of 909, 525, 254 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 909, 525, 254?

Answer: HCF of 909, 525, 254 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 909, 525, 254 using Euclid's Algorithm?

Answer: For arbitrary numbers 909, 525, 254 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.