Highest Common Factor of 7752, 2039, 19992 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 7752, 2039, 19992 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7752, 2039, 19992 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 7752, 2039, 19992 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 7752, 2039, 19992 is 1.

HCF(7752, 2039, 19992) = 1

HCF of 7752, 2039, 19992 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 7752, 2039, 19992 is 1.

Highest Common Factor of 7752,2039,19992 using Euclid's algorithm

Highest Common Factor of 7752,2039,19992 is 1

Step 1: Since 7752 > 2039, we apply the division lemma to 7752 and 2039, to get

7752 = 2039 x 3 + 1635

Step 2: Since the reminder 2039 ≠ 0, we apply division lemma to 1635 and 2039, to get

2039 = 1635 x 1 + 404

Step 3: We consider the new divisor 1635 and the new remainder 404, and apply the division lemma to get

1635 = 404 x 4 + 19

We consider the new divisor 404 and the new remainder 19,and apply the division lemma to get

404 = 19 x 21 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7752 and 2039 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(404,19) = HCF(1635,404) = HCF(2039,1635) = HCF(7752,2039) .

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

Step 1: Since 19992 > 1, we apply the division lemma to 19992 and 1, to get

19992 = 1 x 19992 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 19992 is 1

Notice that 1 = HCF(19992,1) .

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Frequently Asked Questions on HCF of 7752, 2039, 19992 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 7752, 2039, 19992?

Answer: HCF of 7752, 2039, 19992 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7752, 2039, 19992 using Euclid's Algorithm?

Answer: For arbitrary numbers 7752, 2039, 19992 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.