Highest Common Factor of 999, 9780, 5743 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 999, 9780, 5743 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 999, 9780, 5743 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 999, 9780, 5743 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 999, 9780, 5743 is 1.

HCF(999, 9780, 5743) = 1

HCF of 999, 9780, 5743 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 999, 9780, 5743 is 1.

Highest Common Factor of 999,9780,5743 using Euclid's algorithm

Highest Common Factor of 999,9780,5743 is 1

Step 1: Since 9780 > 999, we apply the division lemma to 9780 and 999, to get

9780 = 999 x 9 + 789

Step 2: Since the reminder 999 ≠ 0, we apply division lemma to 789 and 999, to get

999 = 789 x 1 + 210

Step 3: We consider the new divisor 789 and the new remainder 210, and apply the division lemma to get

789 = 210 x 3 + 159

We consider the new divisor 210 and the new remainder 159,and apply the division lemma to get

210 = 159 x 1 + 51

We consider the new divisor 159 and the new remainder 51,and apply the division lemma to get

159 = 51 x 3 + 6

We consider the new divisor 51 and the new remainder 6,and apply the division lemma to get

51 = 6 x 8 + 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 999 and 9780 is 3

Notice that 3 = HCF(6,3) = HCF(51,6) = HCF(159,51) = HCF(210,159) = HCF(789,210) = HCF(999,789) = HCF(9780,999) .

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

Step 1: Since 5743 > 3, we apply the division lemma to 5743 and 3, to get

5743 = 3 x 1914 + 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 5743 is 1

Notice that 1 = HCF(3,1) = HCF(5743,3) .

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Frequently Asked Questions on HCF of 999, 9780, 5743 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 999, 9780, 5743?

Answer: HCF of 999, 9780, 5743 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 999, 9780, 5743 using Euclid's Algorithm?

Answer: For arbitrary numbers 999, 9780, 5743 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.