Highest Common Factor of 666, 61513 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 666, 61513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 666, 61513 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 666, 61513 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 666, 61513 is 1.

HCF(666, 61513) = 1

HCF of 666, 61513 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 666, 61513 is 1.

Highest Common Factor of 666,61513 using Euclid's algorithm

Highest Common Factor of 666,61513 is 1

Step 1: Since 61513 > 666, we apply the division lemma to 61513 and 666, to get

61513 = 666 x 92 + 241

Step 2: Since the reminder 666 ≠ 0, we apply division lemma to 241 and 666, to get

666 = 241 x 2 + 184

Step 3: We consider the new divisor 241 and the new remainder 184, and apply the division lemma to get

241 = 184 x 1 + 57

We consider the new divisor 184 and the new remainder 57,and apply the division lemma to get

184 = 57 x 3 + 13

We consider the new divisor 57 and the new remainder 13,and apply the division lemma to get

57 = 13 x 4 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 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 666 and 61513 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(57,13) = HCF(184,57) = HCF(241,184) = HCF(666,241) = HCF(61513,666) .

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Frequently Asked Questions on HCF of 666, 61513 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 666, 61513?

Answer: HCF of 666, 61513 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 666, 61513 using Euclid's Algorithm?

Answer: For arbitrary numbers 666, 61513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.