Highest Common Factor of 442, 165, 211 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 442, 165, 211 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 442, 165, 211 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 442, 165, 211 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 442, 165, 211 is 1.

HCF(442, 165, 211) = 1

HCF of 442, 165, 211 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 442, 165, 211 is 1.

Highest Common Factor of 442,165,211 using Euclid's algorithm

Highest Common Factor of 442,165,211 is 1

Step 1: Since 442 > 165, we apply the division lemma to 442 and 165, to get

442 = 165 x 2 + 112

Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 112 and 165, to get

165 = 112 x 1 + 53

Step 3: We consider the new divisor 112 and the new remainder 53, and apply the division lemma to get

112 = 53 x 2 + 6

We consider the new divisor 53 and the new remainder 6,and apply the division lemma to get

53 = 6 x 8 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 442 and 165 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(53,6) = HCF(112,53) = HCF(165,112) = HCF(442,165) .

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

Step 1: Since 211 > 1, we apply the division lemma to 211 and 1, to get

211 = 1 x 211 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 211 is 1

Notice that 1 = HCF(211,1) .

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Frequently Asked Questions on HCF of 442, 165, 211 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 442, 165, 211?

Answer: HCF of 442, 165, 211 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 442, 165, 211 using Euclid's Algorithm?

Answer: For arbitrary numbers 442, 165, 211 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.