Highest Common Factor of 384, 976, 285 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, 976, 285 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 384, 976, 285 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, 976, 285 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, 976, 285 is 1.

HCF(384, 976, 285) = 1

HCF of 384, 976, 285 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, 976, 285 is 1.

Highest Common Factor of 384,976,285 using Euclid's algorithm

Highest Common Factor of 384,976,285 is 1

Step 1: Since 976 > 384, we apply the division lemma to 976 and 384, to get

976 = 384 x 2 + 208

Step 2: Since the reminder 384 ≠ 0, we apply division lemma to 208 and 384, to get

384 = 208 x 1 + 176

Step 3: We consider the new divisor 208 and the new remainder 176, and apply the division lemma to get

208 = 176 x 1 + 32

We consider the new divisor 176 and the new remainder 32,and apply the division lemma to get

176 = 32 x 5 + 16

We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get

32 = 16 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 384 and 976 is 16

Notice that 16 = HCF(32,16) = HCF(176,32) = HCF(208,176) = HCF(384,208) = HCF(976,384) .

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

Step 1: Since 285 > 16, we apply the division lemma to 285 and 16, to get

285 = 16 x 17 + 13

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 13 and 16, to get

16 = 13 x 1 + 3

Step 3: We consider the new divisor 13 and the new remainder 3, and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 16 and 285 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(285,16) .

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Frequently Asked Questions on HCF of 384, 976, 285 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, 976, 285?

Answer: HCF of 384, 976, 285 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 384, 976, 285 using Euclid's Algorithm?

Answer: For arbitrary numbers 384, 976, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.