Highest Common Factor of 2004, 2710, 87727 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 2004, 2710, 87727 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2004, 2710, 87727 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 2004, 2710, 87727 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 2004, 2710, 87727 is 1.

HCF(2004, 2710, 87727) = 1

HCF of 2004, 2710, 87727 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 2004, 2710, 87727 is 1.

Highest Common Factor of 2004,2710,87727 using Euclid's algorithm

Highest Common Factor of 2004,2710,87727 is 1

Step 1: Since 2710 > 2004, we apply the division lemma to 2710 and 2004, to get

2710 = 2004 x 1 + 706

Step 2: Since the reminder 2004 ≠ 0, we apply division lemma to 706 and 2004, to get

2004 = 706 x 2 + 592

Step 3: We consider the new divisor 706 and the new remainder 592, and apply the division lemma to get

706 = 592 x 1 + 114

We consider the new divisor 592 and the new remainder 114,and apply the division lemma to get

592 = 114 x 5 + 22

We consider the new divisor 114 and the new remainder 22,and apply the division lemma to get

114 = 22 x 5 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 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 2004 and 2710 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(114,22) = HCF(592,114) = HCF(706,592) = HCF(2004,706) = HCF(2710,2004) .

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

Step 1: Since 87727 > 2, we apply the division lemma to 87727 and 2, to get

87727 = 2 x 43863 + 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 87727 is 1

Notice that 1 = HCF(2,1) = HCF(87727,2) .

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Frequently Asked Questions on HCF of 2004, 2710, 87727 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 2004, 2710, 87727?

Answer: HCF of 2004, 2710, 87727 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2004, 2710, 87727 using Euclid's Algorithm?

Answer: For arbitrary numbers 2004, 2710, 87727 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.