Highest Common Factor of 2078, 5065, 39364 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 2078, 5065, 39364 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2078, 5065, 39364 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 2078, 5065, 39364 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 2078, 5065, 39364 is 1.

HCF(2078, 5065, 39364) = 1

HCF of 2078, 5065, 39364 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 2078, 5065, 39364 is 1.

Highest Common Factor of 2078,5065,39364 using Euclid's algorithm

Highest Common Factor of 2078,5065,39364 is 1

Step 1: Since 5065 > 2078, we apply the division lemma to 5065 and 2078, to get

5065 = 2078 x 2 + 909

Step 2: Since the reminder 2078 ≠ 0, we apply division lemma to 909 and 2078, to get

2078 = 909 x 2 + 260

Step 3: We consider the new divisor 909 and the new remainder 260, and apply the division lemma to get

909 = 260 x 3 + 129

We consider the new divisor 260 and the new remainder 129,and apply the division lemma to get

260 = 129 x 2 + 2

We consider the new divisor 129 and the new remainder 2,and apply the division lemma to get

129 = 2 x 64 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 2078 and 5065 is 1

Notice that 1 = HCF(2,1) = HCF(129,2) = HCF(260,129) = HCF(909,260) = HCF(2078,909) = HCF(5065,2078) .

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

Step 1: Since 39364 > 1, we apply the division lemma to 39364 and 1, to get

39364 = 1 x 39364 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 39364 is 1

Notice that 1 = HCF(39364,1) .

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Frequently Asked Questions on HCF of 2078, 5065, 39364 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 2078, 5065, 39364?

Answer: HCF of 2078, 5065, 39364 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2078, 5065, 39364 using Euclid's Algorithm?

Answer: For arbitrary numbers 2078, 5065, 39364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.