Highest Common Factor of 1977, 2820, 90233 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 1977, 2820, 90233 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1977, 2820, 90233 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 1977, 2820, 90233 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 1977, 2820, 90233 is 1.

HCF(1977, 2820, 90233) = 1

HCF of 1977, 2820, 90233 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 1977, 2820, 90233 is 1.

Highest Common Factor of 1977,2820,90233 using Euclid's algorithm

Highest Common Factor of 1977,2820,90233 is 1

Step 1: Since 2820 > 1977, we apply the division lemma to 2820 and 1977, to get

2820 = 1977 x 1 + 843

Step 2: Since the reminder 1977 ≠ 0, we apply division lemma to 843 and 1977, to get

1977 = 843 x 2 + 291

Step 3: We consider the new divisor 843 and the new remainder 291, and apply the division lemma to get

843 = 291 x 2 + 261

We consider the new divisor 291 and the new remainder 261,and apply the division lemma to get

291 = 261 x 1 + 30

We consider the new divisor 261 and the new remainder 30,and apply the division lemma to get

261 = 30 x 8 + 21

We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get

30 = 21 x 1 + 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 1977 and 2820 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(261,30) = HCF(291,261) = HCF(843,291) = HCF(1977,843) = HCF(2820,1977) .

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

Step 1: Since 90233 > 3, we apply the division lemma to 90233 and 3, to get

90233 = 3 x 30077 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 90233 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(90233,3) .

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Frequently Asked Questions on HCF of 1977, 2820, 90233 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 1977, 2820, 90233?

Answer: HCF of 1977, 2820, 90233 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1977, 2820, 90233 using Euclid's Algorithm?

Answer: For arbitrary numbers 1977, 2820, 90233 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.