Highest Common Factor of 665, 423, 115 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, 423, 115 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 665, 423, 115 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, 423, 115 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, 423, 115 is 1.

HCF(665, 423, 115) = 1

HCF of 665, 423, 115 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, 423, 115 is 1.

Highest Common Factor of 665,423,115 using Euclid's algorithm

Highest Common Factor of 665,423,115 is 1

Step 1: Since 665 > 423, we apply the division lemma to 665 and 423, to get

665 = 423 x 1 + 242

Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 242 and 423, to get

423 = 242 x 1 + 181

Step 3: We consider the new divisor 242 and the new remainder 181, and apply the division lemma to get

242 = 181 x 1 + 61

We consider the new divisor 181 and the new remainder 61,and apply the division lemma to get

181 = 61 x 2 + 59

We consider the new divisor 61 and the new remainder 59,and apply the division lemma to get

61 = 59 x 1 + 2

We consider the new divisor 59 and the new remainder 2,and apply the division lemma to get

59 = 2 x 29 + 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 423 is 1

Notice that 1 = HCF(2,1) = HCF(59,2) = HCF(61,59) = HCF(181,61) = HCF(242,181) = HCF(423,242) = HCF(665,423) .

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

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

115 = 1 x 115 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 115 is 1

Notice that 1 = HCF(115,1) .

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Frequently Asked Questions on HCF of 665, 423, 115 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, 423, 115?

Answer: HCF of 665, 423, 115 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 665, 423, 115 using Euclid's Algorithm?

Answer: For arbitrary numbers 665, 423, 115 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.