Highest Common Factor of 384, 655, 21 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 384, 655, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 384, 655, 21 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 384, 655, 21 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 384, 655, 21 is 1.

HCF(384, 655, 21) = 1

HCF of 384, 655, 21 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 384, 655, 21 is 1.

Highest Common Factor of 384,655,21 using Euclid's algorithm

Highest Common Factor of 384,655,21 is 1

Step 1: Since 655 > 384, we apply the division lemma to 655 and 384, to get

655 = 384 x 1 + 271

Step 2: Since the reminder 384 ≠ 0, we apply division lemma to 271 and 384, to get

384 = 271 x 1 + 113

Step 3: We consider the new divisor 271 and the new remainder 113, and apply the division lemma to get

271 = 113 x 2 + 45

We consider the new divisor 113 and the new remainder 45,and apply the division lemma to get

113 = 45 x 2 + 23

We consider the new divisor 45 and the new remainder 23,and apply the division lemma to get

45 = 23 x 1 + 22

We consider the new divisor 23 and the new remainder 22,and apply the division lemma to get

23 = 22 x 1 + 1

We consider the new divisor 22 and the new remainder 1,and apply the division lemma to get

22 = 1 x 22 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 384 and 655 is 1

Notice that 1 = HCF(22,1) = HCF(23,22) = HCF(45,23) = HCF(113,45) = HCF(271,113) = HCF(384,271) = HCF(655,384) .

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

Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get

21 = 1 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1

Notice that 1 = HCF(21,1) .

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Frequently Asked Questions on HCF of 384, 655, 21 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 384, 655, 21?

Answer: HCF of 384, 655, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 384, 655, 21 using Euclid's Algorithm?

Answer: For arbitrary numbers 384, 655, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.