Highest Common Factor of 1974, 2747, 33020 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 1974, 2747, 33020 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1974, 2747, 33020 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 1974, 2747, 33020 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 1974, 2747, 33020 is 1.

HCF(1974, 2747, 33020) = 1

HCF of 1974, 2747, 33020 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 1974, 2747, 33020 is 1.

Highest Common Factor of 1974,2747,33020 using Euclid's algorithm

Highest Common Factor of 1974,2747,33020 is 1

Step 1: Since 2747 > 1974, we apply the division lemma to 2747 and 1974, to get

2747 = 1974 x 1 + 773

Step 2: Since the reminder 1974 ≠ 0, we apply division lemma to 773 and 1974, to get

1974 = 773 x 2 + 428

Step 3: We consider the new divisor 773 and the new remainder 428, and apply the division lemma to get

773 = 428 x 1 + 345

We consider the new divisor 428 and the new remainder 345,and apply the division lemma to get

428 = 345 x 1 + 83

We consider the new divisor 345 and the new remainder 83,and apply the division lemma to get

345 = 83 x 4 + 13

We consider the new divisor 83 and the new remainder 13,and apply the division lemma to get

83 = 13 x 6 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 1974 and 2747 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(83,13) = HCF(345,83) = HCF(428,345) = HCF(773,428) = HCF(1974,773) = HCF(2747,1974) .

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

Step 1: Since 33020 > 1, we apply the division lemma to 33020 and 1, to get

33020 = 1 x 33020 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 33020 is 1

Notice that 1 = HCF(33020,1) .

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Frequently Asked Questions on HCF of 1974, 2747, 33020 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 1974, 2747, 33020?

Answer: HCF of 1974, 2747, 33020 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1974, 2747, 33020 using Euclid's Algorithm?

Answer: For arbitrary numbers 1974, 2747, 33020 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.