Highest Common Factor of 992, 5758, 4003 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 992, 5758, 4003 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 992, 5758, 4003 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 992, 5758, 4003 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 992, 5758, 4003 is 1.

HCF(992, 5758, 4003) = 1

HCF of 992, 5758, 4003 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 992, 5758, 4003 is 1.

Highest Common Factor of 992,5758,4003 using Euclid's algorithm

Highest Common Factor of 992,5758,4003 is 1

Step 1: Since 5758 > 992, we apply the division lemma to 5758 and 992, to get

5758 = 992 x 5 + 798

Step 2: Since the reminder 992 ≠ 0, we apply division lemma to 798 and 992, to get

992 = 798 x 1 + 194

Step 3: We consider the new divisor 798 and the new remainder 194, and apply the division lemma to get

798 = 194 x 4 + 22

We consider the new divisor 194 and the new remainder 22,and apply the division lemma to get

194 = 22 x 8 + 18

We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get

22 = 18 x 1 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 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 992 and 5758 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(194,22) = HCF(798,194) = HCF(992,798) = HCF(5758,992) .

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

Step 1: Since 4003 > 2, we apply the division lemma to 4003 and 2, to get

4003 = 2 x 2001 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 4003 is 1

Notice that 1 = HCF(2,1) = HCF(4003,2) .

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Frequently Asked Questions on HCF of 992, 5758, 4003 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 992, 5758, 4003?

Answer: HCF of 992, 5758, 4003 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 992, 5758, 4003 using Euclid's Algorithm?

Answer: For arbitrary numbers 992, 5758, 4003 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.