Highest Common Factor of 665, 383, 80 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, 383, 80 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 665, 383, 80 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, 383, 80 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, 383, 80 is 1.

HCF(665, 383, 80) = 1

HCF of 665, 383, 80 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, 383, 80 is 1.

Highest Common Factor of 665,383,80 using Euclid's algorithm

Highest Common Factor of 665,383,80 is 1

Step 1: Since 665 > 383, we apply the division lemma to 665 and 383, to get

665 = 383 x 1 + 282

Step 2: Since the reminder 383 ≠ 0, we apply division lemma to 282 and 383, to get

383 = 282 x 1 + 101

Step 3: We consider the new divisor 282 and the new remainder 101, and apply the division lemma to get

282 = 101 x 2 + 80

We consider the new divisor 101 and the new remainder 80,and apply the division lemma to get

101 = 80 x 1 + 21

We consider the new divisor 80 and the new remainder 21,and apply the division lemma to get

80 = 21 x 3 + 17

We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get

21 = 17 x 1 + 4

We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get

17 = 4 x 4 + 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 665 and 383 is 1

Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(80,21) = HCF(101,80) = HCF(282,101) = HCF(383,282) = HCF(665,383) .

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

Step 1: Since 80 > 1, we apply the division lemma to 80 and 1, to get

80 = 1 x 80 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 80 is 1

Notice that 1 = HCF(80,1) .

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Frequently Asked Questions on HCF of 665, 383, 80 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, 383, 80?

Answer: HCF of 665, 383, 80 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 665, 383, 80 using Euclid's Algorithm?

Answer: For arbitrary numbers 665, 383, 80 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.