Highest Common Factor of 759, 115, 658 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 759, 115, 658 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 759, 115, 658 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 759, 115, 658 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 759, 115, 658 is 1.

HCF(759, 115, 658) = 1

HCF of 759, 115, 658 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 759, 115, 658 is 1.

Highest Common Factor of 759,115,658 using Euclid's algorithm

Highest Common Factor of 759,115,658 is 1

Step 1: Since 759 > 115, we apply the division lemma to 759 and 115, to get

759 = 115 x 6 + 69

Step 2: Since the reminder 115 ≠ 0, we apply division lemma to 69 and 115, to get

115 = 69 x 1 + 46

Step 3: We consider the new divisor 69 and the new remainder 46, and apply the division lemma to get

69 = 46 x 1 + 23

We consider the new divisor 46 and the new remainder 23, and apply the division lemma to get

46 = 23 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 759 and 115 is 23

Notice that 23 = HCF(46,23) = HCF(69,46) = HCF(115,69) = HCF(759,115) .

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

Step 1: Since 658 > 23, we apply the division lemma to 658 and 23, to get

658 = 23 x 28 + 14

Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 14 and 23, to get

23 = 14 x 1 + 9

Step 3: We consider the new divisor 14 and the new remainder 9, and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 23 and 658 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(23,14) = HCF(658,23) .

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Frequently Asked Questions on HCF of 759, 115, 658 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 759, 115, 658?

Answer: HCF of 759, 115, 658 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 759, 115, 658 using Euclid's Algorithm?

Answer: For arbitrary numbers 759, 115, 658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.