Highest Common Factor of 1417, 7727, 65139 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 1417, 7727, 65139 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1417, 7727, 65139 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 1417, 7727, 65139 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 1417, 7727, 65139 is 1.

HCF(1417, 7727, 65139) = 1

HCF of 1417, 7727, 65139 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 1417, 7727, 65139 is 1.

Highest Common Factor of 1417,7727,65139 using Euclid's algorithm

Highest Common Factor of 1417,7727,65139 is 1

Step 1: Since 7727 > 1417, we apply the division lemma to 7727 and 1417, to get

7727 = 1417 x 5 + 642

Step 2: Since the reminder 1417 ≠ 0, we apply division lemma to 642 and 1417, to get

1417 = 642 x 2 + 133

Step 3: We consider the new divisor 642 and the new remainder 133, and apply the division lemma to get

642 = 133 x 4 + 110

We consider the new divisor 133 and the new remainder 110,and apply the division lemma to get

133 = 110 x 1 + 23

We consider the new divisor 110 and the new remainder 23,and apply the division lemma to get

110 = 23 x 4 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 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 1417 and 7727 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(110,23) = HCF(133,110) = HCF(642,133) = HCF(1417,642) = HCF(7727,1417) .

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

Step 1: Since 65139 > 1, we apply the division lemma to 65139 and 1, to get

65139 = 1 x 65139 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 65139 is 1

Notice that 1 = HCF(65139,1) .

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Frequently Asked Questions on HCF of 1417, 7727, 65139 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 1417, 7727, 65139?

Answer: HCF of 1417, 7727, 65139 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1417, 7727, 65139 using Euclid's Algorithm?

Answer: For arbitrary numbers 1417, 7727, 65139 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.