Highest Common Factor of 5835, 7440, 99948 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 5835, 7440, 99948 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 5835, 7440, 99948 is 3 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 5835, 7440, 99948 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 5835, 7440, 99948 is 3.

HCF(5835, 7440, 99948) = 3

HCF of 5835, 7440, 99948 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 5835, 7440, 99948 is 3.

Highest Common Factor of 5835,7440,99948 using Euclid's algorithm

Highest Common Factor of 5835,7440,99948 is 3

Step 1: Since 7440 > 5835, we apply the division lemma to 7440 and 5835, to get

7440 = 5835 x 1 + 1605

Step 2: Since the reminder 5835 ≠ 0, we apply division lemma to 1605 and 5835, to get

5835 = 1605 x 3 + 1020

Step 3: We consider the new divisor 1605 and the new remainder 1020, and apply the division lemma to get

1605 = 1020 x 1 + 585

We consider the new divisor 1020 and the new remainder 585,and apply the division lemma to get

1020 = 585 x 1 + 435

We consider the new divisor 585 and the new remainder 435,and apply the division lemma to get

585 = 435 x 1 + 150

We consider the new divisor 435 and the new remainder 150,and apply the division lemma to get

435 = 150 x 2 + 135

We consider the new divisor 150 and the new remainder 135,and apply the division lemma to get

150 = 135 x 1 + 15

We consider the new divisor 135 and the new remainder 15,and apply the division lemma to get

135 = 15 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 5835 and 7440 is 15

Notice that 15 = HCF(135,15) = HCF(150,135) = HCF(435,150) = HCF(585,435) = HCF(1020,585) = HCF(1605,1020) = HCF(5835,1605) = HCF(7440,5835) .

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

Step 1: Since 99948 > 15, we apply the division lemma to 99948 and 15, to get

99948 = 15 x 6663 + 3

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 3 and 15, to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 99948 is 3

Notice that 3 = HCF(15,3) = HCF(99948,15) .

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Frequently Asked Questions on HCF of 5835, 7440, 99948 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 5835, 7440, 99948?

Answer: HCF of 5835, 7440, 99948 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5835, 7440, 99948 using Euclid's Algorithm?

Answer: For arbitrary numbers 5835, 7440, 99948 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.