Highest Common Factor of 9874, 7705 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 9874, 7705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9874, 7705 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 9874, 7705 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 9874, 7705 is 1.

HCF(9874, 7705) = 1

HCF of 9874, 7705 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 9874, 7705 is 1.

Highest Common Factor of 9874,7705 using Euclid's algorithm

Highest Common Factor of 9874,7705 is 1

Step 1: Since 9874 > 7705, we apply the division lemma to 9874 and 7705, to get

9874 = 7705 x 1 + 2169

Step 2: Since the reminder 7705 ≠ 0, we apply division lemma to 2169 and 7705, to get

7705 = 2169 x 3 + 1198

Step 3: We consider the new divisor 2169 and the new remainder 1198, and apply the division lemma to get

2169 = 1198 x 1 + 971

We consider the new divisor 1198 and the new remainder 971,and apply the division lemma to get

1198 = 971 x 1 + 227

We consider the new divisor 971 and the new remainder 227,and apply the division lemma to get

971 = 227 x 4 + 63

We consider the new divisor 227 and the new remainder 63,and apply the division lemma to get

227 = 63 x 3 + 38

We consider the new divisor 63 and the new remainder 38,and apply the division lemma to get

63 = 38 x 1 + 25

We consider the new divisor 38 and the new remainder 25,and apply the division lemma to get

38 = 25 x 1 + 13

We consider the new divisor 25 and the new remainder 13,and apply the division lemma to get

25 = 13 x 1 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9874 and 7705 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(25,13) = HCF(38,25) = HCF(63,38) = HCF(227,63) = HCF(971,227) = HCF(1198,971) = HCF(2169,1198) = HCF(7705,2169) = HCF(9874,7705) .

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Frequently Asked Questions on HCF of 9874, 7705 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 9874, 7705?

Answer: HCF of 9874, 7705 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9874, 7705 using Euclid's Algorithm?

Answer: For arbitrary numbers 9874, 7705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.