Highest Common Factor of 3161, 9310, 43006 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 3161, 9310, 43006 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3161, 9310, 43006 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 3161, 9310, 43006 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 3161, 9310, 43006 is 1.

HCF(3161, 9310, 43006) = 1

HCF of 3161, 9310, 43006 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 3161, 9310, 43006 is 1.

Highest Common Factor of 3161,9310,43006 using Euclid's algorithm

Highest Common Factor of 3161,9310,43006 is 1

Step 1: Since 9310 > 3161, we apply the division lemma to 9310 and 3161, to get

9310 = 3161 x 2 + 2988

Step 2: Since the reminder 3161 ≠ 0, we apply division lemma to 2988 and 3161, to get

3161 = 2988 x 1 + 173

Step 3: We consider the new divisor 2988 and the new remainder 173, and apply the division lemma to get

2988 = 173 x 17 + 47

We consider the new divisor 173 and the new remainder 47,and apply the division lemma to get

173 = 47 x 3 + 32

We consider the new divisor 47 and the new remainder 32,and apply the division lemma to get

47 = 32 x 1 + 15

We consider the new divisor 32 and the new remainder 15,and apply the division lemma to get

32 = 15 x 2 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 3161 and 9310 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(32,15) = HCF(47,32) = HCF(173,47) = HCF(2988,173) = HCF(3161,2988) = HCF(9310,3161) .

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

Step 1: Since 43006 > 1, we apply the division lemma to 43006 and 1, to get

43006 = 1 x 43006 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 43006 is 1

Notice that 1 = HCF(43006,1) .

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Frequently Asked Questions on HCF of 3161, 9310, 43006 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 3161, 9310, 43006?

Answer: HCF of 3161, 9310, 43006 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3161, 9310, 43006 using Euclid's Algorithm?

Answer: For arbitrary numbers 3161, 9310, 43006 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.