Highest Common Factor of 7107, 9800 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 7107, 9800 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7107, 9800 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 7107, 9800 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 7107, 9800 is 1.

HCF(7107, 9800) = 1

HCF of 7107, 9800 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 7107, 9800 is 1.

Highest Common Factor of 7107,9800 using Euclid's algorithm

Highest Common Factor of 7107,9800 is 1

Step 1: Since 9800 > 7107, we apply the division lemma to 9800 and 7107, to get

9800 = 7107 x 1 + 2693

Step 2: Since the reminder 7107 ≠ 0, we apply division lemma to 2693 and 7107, to get

7107 = 2693 x 2 + 1721

Step 3: We consider the new divisor 2693 and the new remainder 1721, and apply the division lemma to get

2693 = 1721 x 1 + 972

We consider the new divisor 1721 and the new remainder 972,and apply the division lemma to get

1721 = 972 x 1 + 749

We consider the new divisor 972 and the new remainder 749,and apply the division lemma to get

972 = 749 x 1 + 223

We consider the new divisor 749 and the new remainder 223,and apply the division lemma to get

749 = 223 x 3 + 80

We consider the new divisor 223 and the new remainder 80,and apply the division lemma to get

223 = 80 x 2 + 63

We consider the new divisor 80 and the new remainder 63,and apply the division lemma to get

80 = 63 x 1 + 17

We consider the new divisor 63 and the new remainder 17,and apply the division lemma to get

63 = 17 x 3 + 12

We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get

17 = 12 x 1 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 7107 and 9800 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(63,17) = HCF(80,63) = HCF(223,80) = HCF(749,223) = HCF(972,749) = HCF(1721,972) = HCF(2693,1721) = HCF(7107,2693) = HCF(9800,7107) .

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Frequently Asked Questions on HCF of 7107, 9800 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 7107, 9800?

Answer: HCF of 7107, 9800 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7107, 9800 using Euclid's Algorithm?

Answer: For arbitrary numbers 7107, 9800 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.