Highest Common Factor of 385, 667, 23 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 385, 667, 23 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 385, 667, 23 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 385, 667, 23 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 385, 667, 23 is 1.

HCF(385, 667, 23) = 1

HCF of 385, 667, 23 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 385, 667, 23 is 1.

Highest Common Factor of 385,667,23 using Euclid's algorithm

Highest Common Factor of 385,667,23 is 1

Step 1: Since 667 > 385, we apply the division lemma to 667 and 385, to get

667 = 385 x 1 + 282

Step 2: Since the reminder 385 ≠ 0, we apply division lemma to 282 and 385, to get

385 = 282 x 1 + 103

Step 3: We consider the new divisor 282 and the new remainder 103, and apply the division lemma to get

282 = 103 x 2 + 76

We consider the new divisor 103 and the new remainder 76,and apply the division lemma to get

103 = 76 x 1 + 27

We consider the new divisor 76 and the new remainder 27,and apply the division lemma to get

76 = 27 x 2 + 22

We consider the new divisor 27 and the new remainder 22,and apply the division lemma to get

27 = 22 x 1 + 5

We consider the new divisor 22 and the new remainder 5,and apply the division lemma to get

22 = 5 x 4 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 385 and 667 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(22,5) = HCF(27,22) = HCF(76,27) = HCF(103,76) = HCF(282,103) = HCF(385,282) = HCF(667,385) .

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

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

23 = 1 x 23 + 0

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

Notice that 1 = HCF(23,1) .

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Frequently Asked Questions on HCF of 385, 667, 23 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 385, 667, 23?

Answer: HCF of 385, 667, 23 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 385, 667, 23 using Euclid's Algorithm?

Answer: For arbitrary numbers 385, 667, 23 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.