Highest Common Factor of 7121, 9824 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 7121, 9824 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7121, 9824 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 7121, 9824 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 7121, 9824 is 1.

HCF(7121, 9824) = 1

HCF of 7121, 9824 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 7121, 9824 is 1.

Highest Common Factor of 7121,9824 using Euclid's algorithm

Highest Common Factor of 7121,9824 is 1

Step 1: Since 9824 > 7121, we apply the division lemma to 9824 and 7121, to get

9824 = 7121 x 1 + 2703

Step 2: Since the reminder 7121 ≠ 0, we apply division lemma to 2703 and 7121, to get

7121 = 2703 x 2 + 1715

Step 3: We consider the new divisor 2703 and the new remainder 1715, and apply the division lemma to get

2703 = 1715 x 1 + 988

We consider the new divisor 1715 and the new remainder 988,and apply the division lemma to get

1715 = 988 x 1 + 727

We consider the new divisor 988 and the new remainder 727,and apply the division lemma to get

988 = 727 x 1 + 261

We consider the new divisor 727 and the new remainder 261,and apply the division lemma to get

727 = 261 x 2 + 205

We consider the new divisor 261 and the new remainder 205,and apply the division lemma to get

261 = 205 x 1 + 56

We consider the new divisor 205 and the new remainder 56,and apply the division lemma to get

205 = 56 x 3 + 37

We consider the new divisor 56 and the new remainder 37,and apply the division lemma to get

56 = 37 x 1 + 19

We consider the new divisor 37 and the new remainder 19,and apply the division lemma to get

37 = 19 x 1 + 18

We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get

19 = 18 x 1 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7121 and 9824 is 1

Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(56,37) = HCF(205,56) = HCF(261,205) = HCF(727,261) = HCF(988,727) = HCF(1715,988) = HCF(2703,1715) = HCF(7121,2703) = HCF(9824,7121) .

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Frequently Asked Questions on HCF of 7121, 9824 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 7121, 9824?

Answer: HCF of 7121, 9824 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7121, 9824 using Euclid's Algorithm?

Answer: For arbitrary numbers 7121, 9824 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.