Highest Common Factor of 2083, 7760 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 2083, 7760 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2083, 7760 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 2083, 7760 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 2083, 7760 is 1.

HCF(2083, 7760) = 1

HCF of 2083, 7760 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 2083, 7760 is 1.

Highest Common Factor of 2083,7760 using Euclid's algorithm

Highest Common Factor of 2083,7760 is 1

Step 1: Since 7760 > 2083, we apply the division lemma to 7760 and 2083, to get

7760 = 2083 x 3 + 1511

Step 2: Since the reminder 2083 ≠ 0, we apply division lemma to 1511 and 2083, to get

2083 = 1511 x 1 + 572

Step 3: We consider the new divisor 1511 and the new remainder 572, and apply the division lemma to get

1511 = 572 x 2 + 367

We consider the new divisor 572 and the new remainder 367,and apply the division lemma to get

572 = 367 x 1 + 205

We consider the new divisor 367 and the new remainder 205,and apply the division lemma to get

367 = 205 x 1 + 162

We consider the new divisor 205 and the new remainder 162,and apply the division lemma to get

205 = 162 x 1 + 43

We consider the new divisor 162 and the new remainder 43,and apply the division lemma to get

162 = 43 x 3 + 33

We consider the new divisor 43 and the new remainder 33,and apply the division lemma to get

43 = 33 x 1 + 10

We consider the new divisor 33 and the new remainder 10,and apply the division lemma to get

33 = 10 x 3 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 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 2083 and 7760 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(33,10) = HCF(43,33) = HCF(162,43) = HCF(205,162) = HCF(367,205) = HCF(572,367) = HCF(1511,572) = HCF(2083,1511) = HCF(7760,2083) .

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Frequently Asked Questions on HCF of 2083, 7760 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 2083, 7760?

Answer: HCF of 2083, 7760 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2083, 7760 using Euclid's Algorithm?

Answer: For arbitrary numbers 2083, 7760 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.