Highest Common Factor of 173, 232, 413 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 173, 232, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 173, 232, 413 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 173, 232, 413 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 173, 232, 413 is 1.

HCF(173, 232, 413) = 1

HCF of 173, 232, 413 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 173, 232, 413 is 1.

Highest Common Factor of 173,232,413 using Euclid's algorithm

Highest Common Factor of 173,232,413 is 1

Step 1: Since 232 > 173, we apply the division lemma to 232 and 173, to get

232 = 173 x 1 + 59

Step 2: Since the reminder 173 ≠ 0, we apply division lemma to 59 and 173, to get

173 = 59 x 2 + 55

Step 3: We consider the new divisor 59 and the new remainder 55, and apply the division lemma to get

59 = 55 x 1 + 4

We consider the new divisor 55 and the new remainder 4,and apply the division lemma to get

55 = 4 x 13 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 173 and 232 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(55,4) = HCF(59,55) = HCF(173,59) = HCF(232,173) .

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

Step 1: Since 413 > 1, we apply the division lemma to 413 and 1, to get

413 = 1 x 413 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 413 is 1

Notice that 1 = HCF(413,1) .

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Frequently Asked Questions on HCF of 173, 232, 413 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 173, 232, 413?

Answer: HCF of 173, 232, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 173, 232, 413 using Euclid's Algorithm?

Answer: For arbitrary numbers 173, 232, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.