Highest Common Factor of 353, 908, 173 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 353, 908, 173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 353, 908, 173 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 353, 908, 173 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 353, 908, 173 is 1.

HCF(353, 908, 173) = 1

HCF of 353, 908, 173 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 353, 908, 173 is 1.

Highest Common Factor of 353,908,173 using Euclid's algorithm

Highest Common Factor of 353,908,173 is 1

Step 1: Since 908 > 353, we apply the division lemma to 908 and 353, to get

908 = 353 x 2 + 202

Step 2: Since the reminder 353 ≠ 0, we apply division lemma to 202 and 353, to get

353 = 202 x 1 + 151

Step 3: We consider the new divisor 202 and the new remainder 151, and apply the division lemma to get

202 = 151 x 1 + 51

We consider the new divisor 151 and the new remainder 51,and apply the division lemma to get

151 = 51 x 2 + 49

We consider the new divisor 51 and the new remainder 49,and apply the division lemma to get

51 = 49 x 1 + 2

We consider the new divisor 49 and the new remainder 2,and apply the division lemma to get

49 = 2 x 24 + 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 353 and 908 is 1

Notice that 1 = HCF(2,1) = HCF(49,2) = HCF(51,49) = HCF(151,51) = HCF(202,151) = HCF(353,202) = HCF(908,353) .

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

Step 1: Since 173 > 1, we apply the division lemma to 173 and 1, to get

173 = 1 x 173 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 173 is 1

Notice that 1 = HCF(173,1) .

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Frequently Asked Questions on HCF of 353, 908, 173 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 353, 908, 173?

Answer: HCF of 353, 908, 173 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 353, 908, 173 using Euclid's Algorithm?

Answer: For arbitrary numbers 353, 908, 173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.