Highest Common Factor of 2000, 1267 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 2000, 1267 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2000, 1267 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 2000, 1267 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 2000, 1267 is 1.

HCF(2000, 1267) = 1

HCF of 2000, 1267 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 2000, 1267 is 1.

Highest Common Factor of 2000,1267 using Euclid's algorithm

Highest Common Factor of 2000,1267 is 1

Step 1: Since 2000 > 1267, we apply the division lemma to 2000 and 1267, to get

2000 = 1267 x 1 + 733

Step 2: Since the reminder 1267 ≠ 0, we apply division lemma to 733 and 1267, to get

1267 = 733 x 1 + 534

Step 3: We consider the new divisor 733 and the new remainder 534, and apply the division lemma to get

733 = 534 x 1 + 199

We consider the new divisor 534 and the new remainder 199,and apply the division lemma to get

534 = 199 x 2 + 136

We consider the new divisor 199 and the new remainder 136,and apply the division lemma to get

199 = 136 x 1 + 63

We consider the new divisor 136 and the new remainder 63,and apply the division lemma to get

136 = 63 x 2 + 10

We consider the new divisor 63 and the new remainder 10,and apply the division lemma to get

63 = 10 x 6 + 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 2000 and 1267 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(63,10) = HCF(136,63) = HCF(199,136) = HCF(534,199) = HCF(733,534) = HCF(1267,733) = HCF(2000,1267) .

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Frequently Asked Questions on HCF of 2000, 1267 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 2000, 1267?

Answer: HCF of 2000, 1267 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2000, 1267 using Euclid's Algorithm?

Answer: For arbitrary numbers 2000, 1267 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.