Highest Common Factor of 909, 2415, 8674 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, 2415, 8674 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 909, 2415, 8674 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, 2415, 8674 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, 2415, 8674 is 1.

HCF(909, 2415, 8674) = 1

HCF of 909, 2415, 8674 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, 2415, 8674 is 1.

Highest Common Factor of 909,2415,8674 using Euclid's algorithm

Highest Common Factor of 909,2415,8674 is 1

Step 1: Since 2415 > 909, we apply the division lemma to 2415 and 909, to get

2415 = 909 x 2 + 597

Step 2: Since the reminder 909 ≠ 0, we apply division lemma to 597 and 909, to get

909 = 597 x 1 + 312

Step 3: We consider the new divisor 597 and the new remainder 312, and apply the division lemma to get

597 = 312 x 1 + 285

We consider the new divisor 312 and the new remainder 285,and apply the division lemma to get

312 = 285 x 1 + 27

We consider the new divisor 285 and the new remainder 27,and apply the division lemma to get

285 = 27 x 10 + 15

We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get

27 = 15 x 1 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 909 and 2415 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(285,27) = HCF(312,285) = HCF(597,312) = HCF(909,597) = HCF(2415,909) .

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

Step 1: Since 8674 > 3, we apply the division lemma to 8674 and 3, to get

8674 = 3 x 2891 + 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 8674 is 1

Notice that 1 = HCF(3,1) = HCF(8674,3) .

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Frequently Asked Questions on HCF of 909, 2415, 8674 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, 2415, 8674?

Answer: HCF of 909, 2415, 8674 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 909, 2415, 8674 using Euclid's Algorithm?

Answer: For arbitrary numbers 909, 2415, 8674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.