Highest Common Factor of 165, 214, 220 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 165, 214, 220 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 165, 214, 220 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 165, 214, 220 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 165, 214, 220 is 1.

HCF(165, 214, 220) = 1

HCF of 165, 214, 220 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 165, 214, 220 is 1.

Highest Common Factor of 165,214,220 using Euclid's algorithm

Highest Common Factor of 165,214,220 is 1

Step 1: Since 214 > 165, we apply the division lemma to 214 and 165, to get

214 = 165 x 1 + 49

Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 49 and 165, to get

165 = 49 x 3 + 18

Step 3: We consider the new divisor 49 and the new remainder 18, and apply the division lemma to get

49 = 18 x 2 + 13

We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get

18 = 13 x 1 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 165 and 214 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(49,18) = HCF(165,49) = HCF(214,165) .

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

Step 1: Since 220 > 1, we apply the division lemma to 220 and 1, to get

220 = 1 x 220 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 220 is 1

Notice that 1 = HCF(220,1) .

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Frequently Asked Questions on HCF of 165, 214, 220 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 165, 214, 220?

Answer: HCF of 165, 214, 220 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 165, 214, 220 using Euclid's Algorithm?

Answer: For arbitrary numbers 165, 214, 220 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.