Highest Common Factor of 665, 5134, 5310 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 665, 5134, 5310 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 665, 5134, 5310 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 665, 5134, 5310 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 665, 5134, 5310 is 1.

HCF(665, 5134, 5310) = 1

HCF of 665, 5134, 5310 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 665, 5134, 5310 is 1.

Highest Common Factor of 665,5134,5310 using Euclid's algorithm

Highest Common Factor of 665,5134,5310 is 1

Step 1: Since 5134 > 665, we apply the division lemma to 5134 and 665, to get

5134 = 665 x 7 + 479

Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 479 and 665, to get

665 = 479 x 1 + 186

Step 3: We consider the new divisor 479 and the new remainder 186, and apply the division lemma to get

479 = 186 x 2 + 107

We consider the new divisor 186 and the new remainder 107,and apply the division lemma to get

186 = 107 x 1 + 79

We consider the new divisor 107 and the new remainder 79,and apply the division lemma to get

107 = 79 x 1 + 28

We consider the new divisor 79 and the new remainder 28,and apply the division lemma to get

79 = 28 x 2 + 23

We consider the new divisor 28 and the new remainder 23,and apply the division lemma to get

28 = 23 x 1 + 5

We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get

23 = 5 x 4 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 665 and 5134 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(28,23) = HCF(79,28) = HCF(107,79) = HCF(186,107) = HCF(479,186) = HCF(665,479) = HCF(5134,665) .

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

Step 1: Since 5310 > 1, we apply the division lemma to 5310 and 1, to get

5310 = 1 x 5310 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5310 is 1

Notice that 1 = HCF(5310,1) .

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Frequently Asked Questions on HCF of 665, 5134, 5310 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 665, 5134, 5310?

Answer: HCF of 665, 5134, 5310 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 665, 5134, 5310 using Euclid's Algorithm?

Answer: For arbitrary numbers 665, 5134, 5310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.