Highest Common Factor of 173, 9986, 3639 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 173, 9986, 3639 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 173, 9986, 3639 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 173, 9986, 3639 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 173, 9986, 3639 is 1.

HCF(173, 9986, 3639) = 1

HCF of 173, 9986, 3639 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 173, 9986, 3639 is 1.

Highest Common Factor of 173,9986,3639 using Euclid's algorithm

Highest Common Factor of 173,9986,3639 is 1

Step 1: Since 9986 > 173, we apply the division lemma to 9986 and 173, to get

9986 = 173 x 57 + 125

Step 2: Since the reminder 173 ≠ 0, we apply division lemma to 125 and 173, to get

173 = 125 x 1 + 48

Step 3: We consider the new divisor 125 and the new remainder 48, and apply the division lemma to get

125 = 48 x 2 + 29

We consider the new divisor 48 and the new remainder 29,and apply the division lemma to get

48 = 29 x 1 + 19

We consider the new divisor 29 and the new remainder 19,and apply the division lemma to get

29 = 19 x 1 + 10

We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get

19 = 10 x 1 + 9

We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get

10 = 9 x 1 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 173 and 9986 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(29,19) = HCF(48,29) = HCF(125,48) = HCF(173,125) = HCF(9986,173) .

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

Step 1: Since 3639 > 1, we apply the division lemma to 3639 and 1, to get

3639 = 1 x 3639 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3639 is 1

Notice that 1 = HCF(3639,1) .

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Frequently Asked Questions on HCF of 173, 9986, 3639 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 173, 9986, 3639?

Answer: HCF of 173, 9986, 3639 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 173, 9986, 3639 using Euclid's Algorithm?

Answer: For arbitrary numbers 173, 9986, 3639 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.