Highest Common Factor of 9844, 6700, 10087 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 9844, 6700, 10087 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9844, 6700, 10087 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 9844, 6700, 10087 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 9844, 6700, 10087 is 1.

HCF(9844, 6700, 10087) = 1

HCF of 9844, 6700, 10087 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 9844, 6700, 10087 is 1.

Highest Common Factor of 9844,6700,10087 using Euclid's algorithm

Highest Common Factor of 9844,6700,10087 is 1

Step 1: Since 9844 > 6700, we apply the division lemma to 9844 and 6700, to get

9844 = 6700 x 1 + 3144

Step 2: Since the reminder 6700 ≠ 0, we apply division lemma to 3144 and 6700, to get

6700 = 3144 x 2 + 412

Step 3: We consider the new divisor 3144 and the new remainder 412, and apply the division lemma to get

3144 = 412 x 7 + 260

We consider the new divisor 412 and the new remainder 260,and apply the division lemma to get

412 = 260 x 1 + 152

We consider the new divisor 260 and the new remainder 152,and apply the division lemma to get

260 = 152 x 1 + 108

We consider the new divisor 152 and the new remainder 108,and apply the division lemma to get

152 = 108 x 1 + 44

We consider the new divisor 108 and the new remainder 44,and apply the division lemma to get

108 = 44 x 2 + 20

We consider the new divisor 44 and the new remainder 20,and apply the division lemma to get

44 = 20 x 2 + 4

We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get

20 = 4 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 9844 and 6700 is 4

Notice that 4 = HCF(20,4) = HCF(44,20) = HCF(108,44) = HCF(152,108) = HCF(260,152) = HCF(412,260) = HCF(3144,412) = HCF(6700,3144) = HCF(9844,6700) .

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

Step 1: Since 10087 > 4, we apply the division lemma to 10087 and 4, to get

10087 = 4 x 2521 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 10087 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(10087,4) .

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Frequently Asked Questions on HCF of 9844, 6700, 10087 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 9844, 6700, 10087?

Answer: HCF of 9844, 6700, 10087 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9844, 6700, 10087 using Euclid's Algorithm?

Answer: For arbitrary numbers 9844, 6700, 10087 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.