Highest Common Factor of 9890, 7730, 47871 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 9890, 7730, 47871 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9890, 7730, 47871 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 9890, 7730, 47871 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 9890, 7730, 47871 is 1.

HCF(9890, 7730, 47871) = 1

HCF of 9890, 7730, 47871 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 9890, 7730, 47871 is 1.

Highest Common Factor of 9890,7730,47871 using Euclid's algorithm

Highest Common Factor of 9890,7730,47871 is 1

Step 1: Since 9890 > 7730, we apply the division lemma to 9890 and 7730, to get

9890 = 7730 x 1 + 2160

Step 2: Since the reminder 7730 ≠ 0, we apply division lemma to 2160 and 7730, to get

7730 = 2160 x 3 + 1250

Step 3: We consider the new divisor 2160 and the new remainder 1250, and apply the division lemma to get

2160 = 1250 x 1 + 910

We consider the new divisor 1250 and the new remainder 910,and apply the division lemma to get

1250 = 910 x 1 + 340

We consider the new divisor 910 and the new remainder 340,and apply the division lemma to get

910 = 340 x 2 + 230

We consider the new divisor 340 and the new remainder 230,and apply the division lemma to get

340 = 230 x 1 + 110

We consider the new divisor 230 and the new remainder 110,and apply the division lemma to get

230 = 110 x 2 + 10

We consider the new divisor 110 and the new remainder 10,and apply the division lemma to get

110 = 10 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 9890 and 7730 is 10

Notice that 10 = HCF(110,10) = HCF(230,110) = HCF(340,230) = HCF(910,340) = HCF(1250,910) = HCF(2160,1250) = HCF(7730,2160) = HCF(9890,7730) .

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

Step 1: Since 47871 > 10, we apply the division lemma to 47871 and 10, to get

47871 = 10 x 4787 + 1

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 1 and 10, to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 47871 is 1

Notice that 1 = HCF(10,1) = HCF(47871,10) .

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Frequently Asked Questions on HCF of 9890, 7730, 47871 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 9890, 7730, 47871?

Answer: HCF of 9890, 7730, 47871 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9890, 7730, 47871 using Euclid's Algorithm?

Answer: For arbitrary numbers 9890, 7730, 47871 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.