Highest Common Factor of 352, 217, 221 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 352, 217, 221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 352, 217, 221 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 352, 217, 221 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 352, 217, 221 is 1.

HCF(352, 217, 221) = 1

HCF of 352, 217, 221 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 352, 217, 221 is 1.

Highest Common Factor of 352,217,221 using Euclid's algorithm

Highest Common Factor of 352,217,221 is 1

Step 1: Since 352 > 217, we apply the division lemma to 352 and 217, to get

352 = 217 x 1 + 135

Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 135 and 217, to get

217 = 135 x 1 + 82

Step 3: We consider the new divisor 135 and the new remainder 82, and apply the division lemma to get

135 = 82 x 1 + 53

We consider the new divisor 82 and the new remainder 53,and apply the division lemma to get

82 = 53 x 1 + 29

We consider the new divisor 53 and the new remainder 29,and apply the division lemma to get

53 = 29 x 1 + 24

We consider the new divisor 29 and the new remainder 24,and apply the division lemma to get

29 = 24 x 1 + 5

We consider the new divisor 24 and the new remainder 5,and apply the division lemma to get

24 = 5 x 4 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 352 and 217 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(24,5) = HCF(29,24) = HCF(53,29) = HCF(82,53) = HCF(135,82) = HCF(217,135) = HCF(352,217) .

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

Step 1: Since 221 > 1, we apply the division lemma to 221 and 1, to get

221 = 1 x 221 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 221 is 1

Notice that 1 = HCF(221,1) .

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Frequently Asked Questions on HCF of 352, 217, 221 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 352, 217, 221?

Answer: HCF of 352, 217, 221 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 352, 217, 221 using Euclid's Algorithm?

Answer: For arbitrary numbers 352, 217, 221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.