Highest Common Factor of 9964, 3802, 13584 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 9964, 3802, 13584 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 9964, 3802, 13584 is 2 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 9964, 3802, 13584 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 9964, 3802, 13584 is 2.

HCF(9964, 3802, 13584) = 2

HCF of 9964, 3802, 13584 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 9964, 3802, 13584 is 2.

Highest Common Factor of 9964,3802,13584 using Euclid's algorithm

Highest Common Factor of 9964,3802,13584 is 2

Step 1: Since 9964 > 3802, we apply the division lemma to 9964 and 3802, to get

9964 = 3802 x 2 + 2360

Step 2: Since the reminder 3802 ≠ 0, we apply division lemma to 2360 and 3802, to get

3802 = 2360 x 1 + 1442

Step 3: We consider the new divisor 2360 and the new remainder 1442, and apply the division lemma to get

2360 = 1442 x 1 + 918

We consider the new divisor 1442 and the new remainder 918,and apply the division lemma to get

1442 = 918 x 1 + 524

We consider the new divisor 918 and the new remainder 524,and apply the division lemma to get

918 = 524 x 1 + 394

We consider the new divisor 524 and the new remainder 394,and apply the division lemma to get

524 = 394 x 1 + 130

We consider the new divisor 394 and the new remainder 130,and apply the division lemma to get

394 = 130 x 3 + 4

We consider the new divisor 130 and the new remainder 4,and apply the division lemma to get

130 = 4 x 32 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9964 and 3802 is 2

Notice that 2 = HCF(4,2) = HCF(130,4) = HCF(394,130) = HCF(524,394) = HCF(918,524) = HCF(1442,918) = HCF(2360,1442) = HCF(3802,2360) = HCF(9964,3802) .

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

Step 1: Since 13584 > 2, we apply the division lemma to 13584 and 2, to get

13584 = 2 x 6792 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 13584 is 2

Notice that 2 = HCF(13584,2) .

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Frequently Asked Questions on HCF of 9964, 3802, 13584 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 9964, 3802, 13584?

Answer: HCF of 9964, 3802, 13584 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9964, 3802, 13584 using Euclid's Algorithm?

Answer: For arbitrary numbers 9964, 3802, 13584 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.