Highest Common Factor of 211, 9735, 1040 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 211, 9735, 1040 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 211, 9735, 1040 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 211, 9735, 1040 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 211, 9735, 1040 is 1.

HCF(211, 9735, 1040) = 1

HCF of 211, 9735, 1040 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 211, 9735, 1040 is 1.

Highest Common Factor of 211,9735,1040 using Euclid's algorithm

Highest Common Factor of 211,9735,1040 is 1

Step 1: Since 9735 > 211, we apply the division lemma to 9735 and 211, to get

9735 = 211 x 46 + 29

Step 2: Since the reminder 211 ≠ 0, we apply division lemma to 29 and 211, to get

211 = 29 x 7 + 8

Step 3: We consider the new divisor 29 and the new remainder 8, and apply the division lemma to get

29 = 8 x 3 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 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 211 and 9735 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(29,8) = HCF(211,29) = HCF(9735,211) .

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

Step 1: Since 1040 > 1, we apply the division lemma to 1040 and 1, to get

1040 = 1 x 1040 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1040 is 1

Notice that 1 = HCF(1040,1) .

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Frequently Asked Questions on HCF of 211, 9735, 1040 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 211, 9735, 1040?

Answer: HCF of 211, 9735, 1040 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 211, 9735, 1040 using Euclid's Algorithm?

Answer: For arbitrary numbers 211, 9735, 1040 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.