Highest Common Factor of 1680, 6081, 30750 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 1680, 6081, 30750 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 1680, 6081, 30750 is 3 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 1680, 6081, 30750 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 1680, 6081, 30750 is 3.

HCF(1680, 6081, 30750) = 3

HCF of 1680, 6081, 30750 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 1680, 6081, 30750 is 3.

Highest Common Factor of 1680,6081,30750 using Euclid's algorithm

Highest Common Factor of 1680,6081,30750 is 3

Step 1: Since 6081 > 1680, we apply the division lemma to 6081 and 1680, to get

6081 = 1680 x 3 + 1041

Step 2: Since the reminder 1680 ≠ 0, we apply division lemma to 1041 and 1680, to get

1680 = 1041 x 1 + 639

Step 3: We consider the new divisor 1041 and the new remainder 639, and apply the division lemma to get

1041 = 639 x 1 + 402

We consider the new divisor 639 and the new remainder 402,and apply the division lemma to get

639 = 402 x 1 + 237

We consider the new divisor 402 and the new remainder 237,and apply the division lemma to get

402 = 237 x 1 + 165

We consider the new divisor 237 and the new remainder 165,and apply the division lemma to get

237 = 165 x 1 + 72

We consider the new divisor 165 and the new remainder 72,and apply the division lemma to get

165 = 72 x 2 + 21

We consider the new divisor 72 and the new remainder 21,and apply the division lemma to get

72 = 21 x 3 + 9

We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get

21 = 9 x 2 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1680 and 6081 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(72,21) = HCF(165,72) = HCF(237,165) = HCF(402,237) = HCF(639,402) = HCF(1041,639) = HCF(1680,1041) = HCF(6081,1680) .

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

Step 1: Since 30750 > 3, we apply the division lemma to 30750 and 3, to get

30750 = 3 x 10250 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 30750 is 3

Notice that 3 = HCF(30750,3) .

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Frequently Asked Questions on HCF of 1680, 6081, 30750 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 1680, 6081, 30750?

Answer: HCF of 1680, 6081, 30750 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1680, 6081, 30750 using Euclid's Algorithm?

Answer: For arbitrary numbers 1680, 6081, 30750 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.