Highest Common Factor of 366, 646, 161 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 366, 646, 161 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 366, 646, 161 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 366, 646, 161 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 366, 646, 161 is 1.

HCF(366, 646, 161) = 1

HCF of 366, 646, 161 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 366, 646, 161 is 1.

Highest Common Factor of 366,646,161 using Euclid's algorithm

Highest Common Factor of 366,646,161 is 1

Step 1: Since 646 > 366, we apply the division lemma to 646 and 366, to get

646 = 366 x 1 + 280

Step 2: Since the reminder 366 ≠ 0, we apply division lemma to 280 and 366, to get

366 = 280 x 1 + 86

Step 3: We consider the new divisor 280 and the new remainder 86, and apply the division lemma to get

280 = 86 x 3 + 22

We consider the new divisor 86 and the new remainder 22,and apply the division lemma to get

86 = 22 x 3 + 20

We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get

22 = 20 x 1 + 2

We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get

20 = 2 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 366 and 646 is 2

Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(86,22) = HCF(280,86) = HCF(366,280) = HCF(646,366) .

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

Step 1: Since 161 > 2, we apply the division lemma to 161 and 2, to get

161 = 2 x 80 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 161 is 1

Notice that 1 = HCF(2,1) = HCF(161,2) .

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Frequently Asked Questions on HCF of 366, 646, 161 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 366, 646, 161?

Answer: HCF of 366, 646, 161 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 366, 646, 161 using Euclid's Algorithm?

Answer: For arbitrary numbers 366, 646, 161 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.